For Hegel, the world is produced of necessity by Geist, but this is not the usual creation by a Supreme Being who is infinite and unknowable. Such a conception of God was an empty category, a 'full stop to knowledge', leading only to the 'bad paths' of intuition or faith, not Reason. Geist is both material and spiritual. Of necessity, a subjective force must create an other if it is really to be a subject. This applies to the mundane ego and the Absolute Subject alike - which leads to a potential critique of the radical subjectivity of Husserl, via Hegel's critique of Kantian morality (see below). 

 The other must be a genuine other, not just the actual appearance of, say, a material world. The real world is therefore contingent to some extent, rather than directly reducible directly to some magic formula of the unfolding of the Idea. In other words, the Idea is not just some simple essence transparently underneath empirical reality. The contingency of the world is necessary.

Reason (capital R, - vernunft or 'speculative reason' rather than just understanding of a given reality, verstand) can perceive the dialectical links between contingent reality and Spirit. The Idea or the Concept is the system that produces the dialectical movements. Subjectivity leads to otherness which leads to alienation (loss of  knowledge or control over the other) which in turn leads to a recovery of otherness. This recovery of otherness involves the understanding of otherness, its 'negation' or 'return' to subjectivity. This dialectic process of otherness and return is discovered in history, and is exemplified in Hegel's work on civilisation, religion, and philosophy. 

 H's own philosophy was the first to recognise the full system, partly because of his brilliance (!) but partly because certain actual developments in society were necesssary before philosophy could gain the truth - 'the owl of Minerva flies only at dusk' - that is, full wisdom about events occurs only in the last stages of actual developments. A stage of social development is necessary before philosphical insights can be  gained.

Logic
 H. attempts to develop not a formal logic (logic as we know it ), but a transcendental logic, after Kant. The basic categories and concepts in this sort of logic are a universal human set by which any human knowledge becomes possible - eg concepts like being, quantity, measure, essence etc. H tries to show that these concepts, as used in ordinary thought and in earlier philosophy are contradictory. This is more than an attempt to show that thought is confused or unclear - contradiction is essential, part of the early stages of developing thought ( and of contradictions in material reality too)
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 H's 'Phenomenology' and his 'Logic(s)' pursue this theme of an 'ascending dialectic', to try to show how contradictions in early, basic, concepts lead to the development of higher and better concepts, and eventually to the Idea (ie to H's concepts). One development has human thought discovering concepts in sequences like this: 

being - determinate being - quantity - quality - measure - essence - Idea. 

In the discussion on logic, causal analysis is rejected as mere verstand, a mere operating at the level of appearances. Causal analysis must be arbitrary, as recognised by Hume - eg X causes Y, but what causes X? Any X is both cause and effect, and the choice of where to start in the causal chain is arbitrary (or produced by utility or contingency). Appearances are produced by Geist manifesting itself - although material reality is contingent to some extent, it is a a mistake to treat it as totally contingent or self-sufficient.

Taylor says the whole discussion begins well enough, showing how contradictions mustl ead to higher level resolutions etc., but it soon begins to drift into smuggling in premisses about just what is a higher order concept, in order to justify H's project.

Morality
Various alternative attempts to ground morality are reviewed, in order to show the necessary emergence of a morality based on free thought. A free thinker will ground his morality on some indubitable starting point, but this must be grounded in a social  practice, in a moral community. As examples of stages in development, Greek morality was firmly embedded in a community life, which was a strength, but it was too parochial, incapable of universalisation, based on city states, city gods etc. (Socrates was condemned, according to H, because he was the first to appeal to universal reason). The Greek community is, in any case, gone forever, and can not (should not) be recaptured. 

Judaism, as a subsequent stage of development, did offer a universal god but an abstract, fierce, and unknowable one. This has one consequence in particular for H - 'the fate of the abstract and universal was to be identified with the rawest particular' (a criticism Marx was to make against Hegel's notion of the State as universal, according to Colletti 1973 - see below). More generally, Judaism eventually produces a classic 'unhappy consciousness' - men are in a world whose purpose is unknown, and this is a block on the development of Reason.

The Enlightenment offered a morality based on subjective groundings and reason - as does Utilitarianism, natural law liberalism, Rousseau's liberalism etc. H offers a very contemporary-sounding criticism here - none of the versions of liberalism can reconcile individual wills and the social. Utilitarianism is condemned as particularly unstable, leading to egoistic demands at the expense of social life (H. sounds very like Durkheim here), and H criticised the English Reform Bill especially. Rousseau's notion of the General Will was on the right lines, but still not related to Geist, still too linked to immediate human wills.

Kantian morality is also a product of Enlightenment: K recommends that we choose potentially universalisable maxims as the basis of our morality. H's criticisms are twofold: (a) this is empty and formal only, since we are asked to choose 'as if' norms were universally applicable - there is no connection with concrete action; (b) if K's maxims ever were operated in a moral community, acting morally would become second nature, losing the essential element of choice (again, very close to Durkheim via Lukes). These problems are classic examples of contradiction for H.

H's solution to all this is to argue that morality is already embodied or grounded or 'objectivised' in sittlichkeit (customs or social morality, almost common-sense or tacit social knowledge). There is still a need for systematisation, of course. In the course of this, H argues that Christianity is the Absolute religion since its creeds embody essential elements of the Idea - eg the Trinity is a representation of movements of the Universal (Father) to the particular (Son) to the recovery of the particular in the community (Holy Ghost). 

Again, the choice of aspects as necessary seems riddled with assumptions. But H claims to have grounded morality in a conception of the social. Individual freedom or autonomy means merely discovering the more-than-egoistic purpose behind it all. H. says that man is finite and must be, like all finite things, in contradiction (this leads to a theodicy). But men can transcend their finitude by discovering their part in the Universal, in the necessary scheme of things, so that they can live on in the community and therefore in Geist. This is the meaning of Jesus who is the one united individual/particular/ universal. H had criticised Christianity once as too 'positive', too concerned with JC as symbol, with his incarnation. The real point is the Pentecost conveying to the community the body of Christ, and thus the notion of unity with the Universal.

The State
 The State embodies morality. The shape of the State reveals the underlying shape of sittlichkeit. Britain is condemned for bulding a State aoround civil society, which can only be based on the utilitiarian clashes of individual wills. France developed an excessive Enlightenment interset in 'absolute freedom'. This leads to some interesting criticisms of the French Revolution (of 1789): the celebration of individual reason and will led to demands for absolute freedom. Given no proper account of a social element (slogans of liberty equality and fraternity  are meaningless in a modern society with divisions of labour etc.), the demand for absolute freedom could only be negative - freedom from an increasing number of constraints. Freedom from constraint became the manifestation of the general will - to resist was to commit an offence against the popular will itself. That was what produced the Terror in France. (Habermas 1974 uses a similar argument against French and American liberals - and also cites this passage from Hegel as an example of the need to consider morality even for Marxists).

A properly organised State must embody the tenets of the Idea: the recognition of the particular and some universal synthesising element. This leads to the idea of a segmented State, with different elements embodied in different 'estates' or 'stande'. Eventually, three stande were isolated as important : (a) peasantry who identify with the particular national body or culture via emotional attachments, custom, sentiment etc.; (b) civil soc. -  utility and private interests plus the utilitarian mechanisms to harmonise them (markets etc). Here, reason as calculation rules.; (c) a 'universal class' (initially an educated aristocracy then an expert civil service) which operates to maintain the nation as a whole using universal Reason. This class contains the other two - contains them politically and socially and contains them in the special sense of aufheben, a dialectical reconciliation and transcendence of other elements. H also believed in the need for a monarchy, as the universalist symbol of the State, and, to give due weight to the need to preserve the concept of the particular and individual, an actual  hereditary person had to be it.
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(Even Taylor recognises this schema as lousy Sociology which ignores social mobility between the stande, and omits all the problems of ensuring that the universal class really does act in the universal interest and not just their own. And of course this is where the Colletti 1973 collection of young Marx criticisms. of H on the State come into their own.)

Notoriously, H allegedly links his ideal State directly to the Prussia of his day. But Taylor says it's not quite as apologetic as it seems. H had praised Prussia for being a progressive monarchy, of the kind he hoped to see, before 1848 and before the acccession of Frederick-William IV. He definitely preferred the German system to Britain or France - and his attacks on reformers in those countries gives him his illiberal reputation. But the 'left-wing Hegelians' who followed him were quick to point out that he wanted a State based solely on Reason, not custom or privilege, and this could be  a source of 'immanent critique' of the existing State. Nevertheless, Marx's 'methodological' point (in Colletti 1973) remains; idealism is always prone to compromise with existing reality?

Final Points
 Just a few scattered thoughts:

1. H defends private property as one of the basic human rights. Owning property is merely as aspect of trying to overcome otherness in the environmemnt! (animals do it by eating the environmenmt - literally returning it to themselves!). Property owning is therefore an ontological necessity.
2.  The notion of contradiction still causes problems for me. Contradictions can be logical and actual/material ( in the shape of actual conflicts etc). But are all relations contradictory necessarily? - H seems to say that essential ones are, from the basic contradiction between Geist and its necessary otherness. He does allow for other kinds of relations - contingent ones - but leaves these for verstand
3. Another helpful sequence to illustrate the sense of anatagonism, contradiction and aufhebung concerns the stages of the development of social relations - H's sociology. Here, the starting point for social relations is the primeval encounter between men who fought until one was dead. This is a means of expressing one's subjectivity, but a frustratingly short-lived (and risky) one. The next stage was slavery, which makes more permanent the subjective  expression over another person. With slavery, the best-known example of a dialectical transcendence occurs - the 'master-slave dialectic'. What happens is that the master comes to lord it over his slave  as much as possible, and this unintentionally makes the slave more and more central to the master's ego - the slave gains power until the two have a much more egalitarian relationship in practice than the formal position admits (the m-s dialectic has been used to understand the sources of resistance by women to men). Eventually, the 'owl of Minerva' does its work, and a new stage of formal equality replaces slavery, as a kind of recognition of the situation. The family, and eventually the State, are fitted into this schema (the 'Jena Programme' which Habermas (1974) so admires - H's liberal phase). This sequence illustrates the notion of 'transformative abolition' of antagonistic relations - masters and slaves do not destroy each other, ending in nothingness, but progress.
4. The concept of negation is used in different senses. Sometimes, it's used in a technical sense to mean the process of opposition and recovery by the Absolute. In  this sense, the Concept is the standing negation of all particulars and all individuals (cf Adorno). Sometimes, negation means something more mundane - the  existence of possible or potential contradictions in something material. For a thing to exist it must have already overcome some of its contradictory possibilities - it has negated (some of) its negations (cf Marcuse's use in Reason and Revolution).

Colletti L (ed) Karl Marx: Early Writings, Harmondsworth: Penguin Books
Habermas J (1974) Theory and Practice, London: Heinemann Educational Books
Marcuse H (1973) Reason and Revolution, London: Routledge and Kegan Paul