Complementary (contradictory/binary) antonymy. Complementary antonyms come in pairs that exhaust all the possibilities within a mixed lexical filed. One denies the other and together they make a whole. E.g. husband -wife', married — single', dead— alive.
Gradation
Also operates with two members of a pair but they can be graded and compared. There is an application of the grammatical comparison in: richer -richest - very rich; hot - cold are two extremes that include several middle members such as: warm, lukewarm, slightly warm, a bit hot, hotter etc. in between the two extremes there are a couple of other lexemes. So if one is not beautiful she or he is not necessarily ugly. The denial of the one is not necessarily affirmation of the other.
Converse (relational) antonymy.
This can be defined as a sort of symmetrical antonymy. It involves a third member besides the pair. E.g. give - take - when you take something there has to be someone to give it to you. Therefore there is something and someone,e.g. John gave the book to Mary. This sentence implies that Mary has taken the book.
Multiple incompatibility
This kind of antonymy involves more than three members. It does not operate in pairs but with multiple number of members. It is relation of opposite-ness that should be established between more than three members. E.g. north -south - east - west. In cards - hearts - diamonds - clubs - spades. Here you can not establish mono-relational opposition. The opposition functions within all the members. For example in the days of the week, months, colours, planets etc. One member in the system enters in relation of opposition with any other member of the system. The denial of one means affirmation of all the other members. Denial of the colour of red is affirmation of all the other colours and vice versa. Whenever there is a small lexical system with more than three elements there is multiple incompatibility.