“Mirror Theory” is the theory that evaluates the number of solutions of affine systems of equalities (=) and non-equalities ( \(\ne \) ) in finite groups. It is deeply related to the security and attacks of many generic cryptographic secret-key schemes, like random Feistel schemes (balanced or unbalanced), Misty schemes, XOR of two pseudo-random bijections to generate a pseudo-random function, etc. In this chapter, we will assume that the groups are abelian. Most of the time in cryptography the group is \(((\mathbb {Z}/2\mathbb {Z})^n, \oplus )\) and this chapter concentrates on these cases. We present here general definitions, some theorems, and many examples and computer simulations.