Combination Reactions:
The reactions in which two substances combine together to form a new compound are called combination reactions. These can be denoted as A+ B → C where either A or B or both A and B should be in the elemental form.

Decomposition reactions:
The reactions in which a compound breaks up into two or more substances at least one of which is in elemental form are called decompositions reactions.

Displacement reactions:
The reactions of the type X + YZ → XZ + Y in which an atom or ion in a compound is displaced by an ion (atom) of another element, such that X and Y are in elemental form are called displacement reactions.
They are of two categories:
1. Metal displacement reactions:
Reactions in which a more electropositive metal displaces a less electropositive metal from its compound. decompositions reactions.

2. Non-metal displacement reactions:
These are reactions in which a non-metal is displaced by another metal or non-metal.

Disproportionation reactions:
These are special type of redox reactions in which an element in one oxidation state is simultaneously oxidised and reduced. Here one of the reactants should contain an element that should exist in at least three oxidation states. The element in the form of reacting substance is in the intermediate oxidation state; and both higher and lower oxidation states of that element are formed in the reaction.
e.g. The decomposition of hydrogen peroxide.

Here the oxygen of peroxide, which is present in -1 state, is converted to zero oxidation state in O2 and to -2 state in H2O.