An Altitude-Azimuth mount is the simplest of telescope mounts.  It consists of two axes with the vertical axis permitting the telescope to be rotated and oriented around the compass bearing or azimuth, and the horizontal axis permitting the angle of elevation or altitude to be adjusted.

Perhaps the simplest form of alt-az mount is the dobsonian mount which is cheap and very simple to fabricate requiring very little engineering.

The main advantage of alt-az mounts is that they are relativelt cheap, simple to set up and use. 

The main drawback of alt-az mounts is that any form of tracking is complicated by the need to drive both axes at different rates.