This course offers a (biased) introduction to proximal methods, a family of algorithms at the forefront of modern numerical optimization. Starting from foundational concepts, we study the proximal point algorithm as a unifying theoretical framework. Attention then shifts to proximal-gradient methods, covering recent advances and convergence analysis under relaxed assumptions in nonconvex settings. For nonsmooth constrained problems, we move beyond classical penalty and barrier approaches to explore contemporary developments in augmented Lagrangian methods and proximal methods. The course prepares students to engage with current research literature and tackle large-scale optimization challenges.