This textbook introduces variational methods and their applications to differential equations to graduate students and researchers interested in differential equations and nonlinear analysis. It serves as a sampling of topics in critical point theory. Coverage includes: minimizations, deformations results, the mountain-pass and saddle-point theorems, critical points under constraints, and issues of compactness. Applications immediately follow each result for easy assimilation by the reader. This straightforward and systematic presentation includes many exercises and examples to motivate the study of variational methods.