This paper presents an effective field theory approach to study generic theories of inflation with a single inflaton field. The methods are used to analyze the leading corrections to the correlation functions of scalar and tensor modes. For scalar modes, the leading corrections to the R correlation function are found to be purely of the k-inflation type. For tensor modes, the leading corrections arise from terms in the action that are quadratic in the curvature, including a parity-violating term that makes the propagation of these modes depend on their helicity. The paper begins by discussing generic theories of inflation, where the inflaton field is canonically normalized and described by a Lagrangian with a potential. It is shown that the expansion rate H and the physical wave number k/a at horizon exit are much less than the Planck mass. The paper then considers the next corrections to the Lagrangian, assuming that the effective field theory is characterized by a mass M, which is much larger than the Planck mass. The effective Lagrangian is then expanded to include higher-derivative terms, which are suppressed by powers of M. The paper then discusses scalar fluctuations, showing that the leading corrections to the Gaussian correlations of R are solely of the k-inflation type. It also considers tensor fluctuations, showing that the leading corrections to the tensor correlation function arise from terms involving the Weyl tensor. The paper also discusses a non-generic example of ghost inflation, where the action has a shift symmetry, and the leading term in the Lagrangian is a power series in the spatial derivatives of the inflaton field. The paper concludes by showing that the effective field theory approach is useful for studying both generic and non-generic theories of inflation, and that the leading corrections to the correlation functions can be calculated using this approach. The results are consistent with observations of the cosmic microwave background and large-scale structure, and provide a justification for using a minimal number of spacetime derivatives in the Lagrangian.This paper presents an effective field theory approach to study generic theories of inflation with a single inflaton field. The methods are used to analyze the leading corrections to the correlation functions of scalar and tensor modes. For scalar modes, the leading corrections to the R correlation function are found to be purely of the k-inflation type. For tensor modes, the leading corrections arise from terms in the action that are quadratic in the curvature, including a parity-violating term that makes the propagation of these modes depend on their helicity. The paper begins by discussing generic theories of inflation, where the inflaton field is canonically normalized and described by a Lagrangian with a potential. It is shown that the expansion rate H and the physical wave number k/a at horizon exit are much less than the Planck mass. The paper then considers the next corrections to the Lagrangian, assuming that the effective field theory is characterized by a mass M, which is much larger than the Planck mass. The effective Lagrangian is then expanded to include higher-derivative terms, which are suppressed by powers of M. The paper then discusses scalar fluctuations, showing that the leading corrections to the Gaussian correlations of R are solely of the k-inflation type. It also considers tensor fluctuations, showing that the leading corrections to the tensor correlation function arise from terms involving the Weyl tensor. The paper also discusses a non-generic example of ghost inflation, where the action has a shift symmetry, and the leading term in the Lagrangian is a power series in the spatial derivatives of the inflaton field. The paper concludes by showing that the effective field theory approach is useful for studying both generic and non-generic theories of inflation, and that the leading corrections to the correlation functions can be calculated using this approach. The results are consistent with observations of the cosmic microwave background and large-scale structure, and provide a justification for using a minimal number of spacetime derivatives in the Lagrangian.