This thesis studies regression-based Monte Carlo methods for pricing American-style options, with a focus on the Least Squares Monte Carlo (LSM) algorithm of Longstaff and Schwartz (2001). After reviewing the theoretical foundations, the LSM algorithm is implemented and validated on single-asset American put options, with particular attention to basis function choice, antithetic variates and convergence diagnostics with respect to the number of paths and exercise dates. The method is then extended to American basket put options written on multiple correlated underlying assets. Two regression specifications for the continuation value are compared: a univariate specification, which regresses on the scalar basket value only, and a multivariate specification, which regresses on the full vector of constituent asset prices.