A swap is called an interest rate swap (IRS), if the whole set of exchanged cash flows involves a common single currency. If the exchange of cash flows involves two currencies, one talks of currency rate swap (CRS) or cross currency rate swap (CCRS). The success of the swap market is significantly due to the security resulting from the universally adopted standard contract documentation from the International Swaps and Derivatives Association (ISDA). This chapter talks about the pricing and (RE) valuation of an IRS swap. Swaps involve both a succession of fixed rate payments and of floating rates payments: even though the former rate is known (fixed in advance) unlike the latter. The IRS and CRS pricing methodology is applicable in the case of swaps whose specifications differ from the vanilla case, that are called second-generation swaps or “exotic” swaps