Set custom keybinding for specific Emacs mode

Though I know how to set a global key-binding in Emacs, I find it hard to even Google out the code for a local (minor-mode specific) key-binding. For instance, I have this code in my .emacs:

;; PDFLaTeX from AucTeX
(global-set-key (kbd "C-c M-p")
		(lambda ()
		  (interactive)
		  (shell-command (concat "pdflatex " buffer-file-name))))

I don't want to set it globally. Is there a function like local-set-key?

I use the following:

(add-hook 'LaTeX-mode-hook
          (lambda () (local-set-key (kbd "C-0") #'run-latexmk)))

to have a bind defined for LaTeX mode alone.

To bind a key in a mode, you need to wait for the mode to be loaded before defining the key. One could require the mode, or use eval-after-load

   (eval-after-load 'latex 
                    '(define-key LaTeX-mode-map [(tab)] 'outline-cycle))

Don't forget either '—eval-after-load is not a macro, so it needs them.

You need to identify the key map for that mode (for example, LaTeX-mode-map) and use the function define-key. As an example, along with activating outline-minor-mode within LaTeX mode, I have:

  (define-key LaTeX-mode-map [(tab)] 'outline-cycle))

In this case the major mode (LaTeX) holds the key binding, but there is also an outline-minor-mode-map.

None of the other answers satisfied my needs. So this may help other people. I wanted Tab to jump to the beginning of the line if I'm in Evil's normal mode (basically this means everywhere in Emacs), but I instead wanted it to cycle between org item states if I am in an org-mode document.

One option was to mess around with separate bindings and constant binding-rebinding whenever I switched buffers (because evil allows only one binding per key in its normal state).

But a more efficient option was to make Tab run my own code which runs the required function based on which major mode the current buffer uses. So if I am in a org buffer, this code runs org-cycle, and otherwise it runs evil-first-non-blank (go to the first non-whitespace character on the line).

The technique I used here can also be used by calling your custom function via global-set-key instead, for people who use regular non-evil Emacs.

For those who don't know Emacs lisp, the first line after the "if" statement is the true-action, and the line after that is the false-action. So if major-mode equals org-mode, we run org-cycle, otherwise we run evil-first-non-blank in all other modes:

  (defun my/tab-jump-or-org-cycle ()
    "jumps to beginning of line in all modes except org mode, where it cycles"
    (interactive)
    (if (equal major-mode 'org-mode)
        (org-cycle)
      (evil-first-non-blank))
    )
  (define-key evil-normal-state-map (kbd "<tab>") 'my/tab-jump-or-org-cycle)