Noncommutative ${\mathrm{\Phi }}^4$ Theory at Two Loops

We study perturbative aspects of noncommutative field theories. This work is arranged in two parts. First, we review noncommutative field theories in general and discuss both canonical and path integral quantization methods. In the second part, we consider the particular example of noncommutative ${\mathrm{\Phi }}^4$ theory in four dimensions and work out the corresponding effective action and discuss renormalizability of the theory, up to two loops.