Transformation

It should be noted that whilst this branch of transfiguration was the first covered in the Hogwarts curriculum, containing simple transfiguration such as Match to needle it also pertained to the most complex and dangerous form of transfiguration too. 

un-Transfiguration

un-transfiguration was the art of reversing a previous transfiguration, being therefore considered both a transfiguration and a counter-spell. It was a mysterious branch of transfiguration. It was known that untransfiguration for failed transformations was taught early. 

Reparifarge was a general spell used to counter the effects of a transformation spell that was poorly performed and only partially transfigured the object in question. This spell was covered in A Beginner’s Guide to Transfiguration.

Switching

Switching was another sub-type of transformation magic. During switching. A physical feature from one of the two targets was switched with that of another, hence the name. It differed from a straight transformation in two ways : firstly, switching targets attected two objects simultaneously; secondly, the change in one of the pairs was dependent on a change in the other. Is it difficult to gauge the relative difficulty of switches exactly compared to other types of transfiguration because the exact year in which they were learned isn’t known, however, professor McGonagall, was impressed when Hermione knew aboutswitches as a first year student, but was disappointed in Neville for not being able to perform even simple switches by fourth year. Therefore students must have started learning switches in second, third, or (early) fourth year (most likely third), earlier than almost all the other branches of transfiguration apart from transformation.

Vanishment

Vanishment was the art of causing things to Vanish; to "make things go into non-being". The difficulty of the Vanishment to be performed positively correlated with the complexity of the organism to be Vanished (for example, snails, as invertebrates, were easier to Vanish than mice, which are mammals). Vanishment was moderately difficult — learned in fifth year — and was considered one of the hardest transfigurations to be tested on in one's O.W.L.

Strangely, only one incantation was needed to Vanish any object - Evanesco , Latin for "disappear" (with the intent of the caster alone directing it), unlike conjurations (which could require a variety of complicated incantations)

Conjuration

Conjuration was the art of conjuring things ("bringing things into being") and hence was the opposite of Vanishment. It was harder than its counterpart, being a N.E.W.T.-level feat, and was taught to sixth and seventh years at Hogwarts. It was also considered to be very advanced magic, though some conjurations were considered simpler then others.

There were numerous restrictions (both in Law and Nature) placed on the art of Conjuration, unlike Vanishment which appeared to be unrestricted. For example, something that was conjured would not last (or, "remain in being"), but it is unknown whether or not something that was vanished could forever remain in non-being if left to its own devices.