Synthesis and decomposition are two types of redox reactions. Synthesis means to make something, whereas decomposition means to break something. The reactions are accompanied by chemical and energy changes. 

Synthesis Reactions

Synthesis reactions are also called combination reactions. It is a reaction in which two or more substances combine to form a complex substance. Synthesis reactions are generally represented as: A + B → AB or A + B → C. The formation of nitrogen dioxide is a synthesis reaction: 2 NO (g) + O₂ (g) → 2 NO₂ (g).

In synthesis reactions, the reactants could be all elements (1), or a combination of an element and a compound (2), or all compounds (3).

1) C (s) + O₂ (g) → CO₂ (g)    
2) 2 CO (g) + O₂ (g) → 2 CO₂ (g) 
3) 2 CaO (s) + 2 H₂O (l) → 2 Ca(OH)₂ (s)

A combination reaction between a metal and a nonmetal always produces an ionic solid. For example, the formation of sodium chloride or table salt from sodium and chlorine is a combination reaction: 2 Na (s) + Cl₂ (g) → 2 NaCl (s).

A synthesis reaction is generally accompanied by the release of energy. In the above example of sodium chloride, 787 kJ of heat energy is released. 

Decomposition Reactions

Oxygen was first discovered by the scientist Joseph Priestley, in 1774, by heating mercury oxide with a burning glass. The reaction was a result of decomposition. Priestley had broken down mercury(II) oxide with heat into its elements. 
The reaction is represented as: 2 HgO (s) → 2 Hg (l) + O₂ (g)

Decomposition reactions involve breaking down a more complex substance into two or more smaller substances. This reaction is often represented as: AB → A + B or C → A + B. Decomposition reactions occur everywhere. For instance, the digestion of proteins, fats, and carbohydrates in our food is an important decomposition reaction. Another example is the decomposition of sodium azide into nitrogen gas. 

The reaction is represented as: 2 NaN₃ (s) → 2 Na (s) + 3 N₂ (g)

In the above reaction, although the coefficient 2 indicates two molecules of sodium azide being decomposed, there is only one reactant. It is, therefore, a decomposition reaction. Similar to the synthesis reaction, in a decomposition reaction, the products formed could be all elements (1), or a combination of elements and compounds (2), or all compounds (3).

1)    2 Al₂O₃ (s) → 4 Al (s) + 3 O₂ (g)
2)    2 KClO₃ (s) → 2 KCl (s) + 3 O₂ (g)
3)    NH₄Cl (s) → NH₃ (g) + HCl (g)