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Define a named function with defun:

(defun square (n)
  (* n n))

(square 5)    ; 25

The parameter list is a vector of names. The body is one or more expressions; the last is the return value.

Optional parameters with &optional:

(defun greet (name &optional (greeting "Hello"))
  (format nil "~a, ~a!" greeting name))

(greet "Ada")               ; "Hello, Ada!"
(greet "Ada" "Hi")          ; "Hi, Ada!"

format nil instead of t returns the string instead of printing.

Anonymous functions with lambda:

(lambda (x) (* x 2))
((lambda (x) (* x 2)) 5)    ; 10 — call inline

Functions are first-class — pass them with #':

(mapcar #'square '(1 2 3 4))    ; (1 4 9 16)

The #' (sharp-quote) extracts the function value from the symbol.