How to check memory usage on Linux

When it comes to optimizing the performance of a Linux system, physical memory is the single most important factor. Naturally, Linux offers a wealth of options to monitor the usage of the precious memory resource. Different tools vary in terms of their monitoring granularity (e.g., system-wide, per-process, per-user), interface (e.g., GUI, command-line, ncurses) or running mode (e.g., interactive, batch mode).