The alt-azimuth mount is the most basic form of telescope mount. Two turning actions allow you to move the scope sideways (changing azimuth) and up or down (changing altitude, or alt). These mounts are, apart from usually being the least expensive, light, strong and easy to set up and use.
The disadvantage of this type of mount is that it does not compensate for the Earth’s rotation and in most cases you will have to adjust both alt and azimuth during observing. This can really be a pain, especially when using the scope at higher magnifications. This type of mount is also more difficult to use when trying to look at objects on, or near, the zenith (directly overhead), as at that point the scope will most likely run into the tripod or pier.