Following is an incomplete list of core functions of Elgg 1.7.x:

get_input
get_input($variable, $default = "", $filter_result = true)
found in /engine/lib/input.php
This function is used to get variables passed in the URL through GET or POST.

get_user_by_username
get_user_by_username($username)
found in /engine/lib/users.php
This function creates an ElggUser object from the username and return this object.