AES is an iterated block cipher. In the standard, the block size is 128 bits, but 192 or 256 bit block sizes are also supported. The key can be 128, 192 or 256 bits, independent of the block size. The number of rounds varies from 10 to 14, depending on the block and key sizes. AES is not a Feistel cipher.
One round of AES consists of 3 layers: a linear mixing layer (diffusion), a non-linear layer and a key addition layer. These 3 layers are accomplished by the following 4 functions: ByteSub, ShiftRow, MixColumn, AddRoundKey. The algorithm has a highly mathematical description.
The S-box is a non-linear (invertible) composition of two mathematical operations (the multiplicative inverse in GF(28) and an affine transformation).
Note that the operation c(x) is (must be) invertible.
