What azimuth description systems are in use? For a time, I thought Azimuth is always direction in degrees, 0 for local, geographic north, 90 for east etc.

Then, trying to observe moonrise I downloaded an app that gave azimuth in values between (if I recall correctly) -180 and 180, and I think "0" corresponded to south. I tried to read up on that and found very little fragmented information. I found other resources that frustrated me with numbers greater than 360, or provided values commonly associated with "West" for azimuth of moonrise and generally it took a bit of searching to find something with plain "degrees from north"

Could someone either post or provide a link to a comprehensive guide to various azimuth angle systems, when and where they are in use, and how to recognize which one is used?
There are many indeed. 

It may be specified from South westwards(0° to 360°), or from North eastwards and westwards(180° to -180°).

The most popular one, as used by Roy and Clarke in "Astronomy : Principles and Practices" is to measure the azimuth from North eastwards 0° to 360°. For a southern hemisphere observer, this system changes to from South eastwards 0° to 360°.

With so much confusion, how do professional astronomers go about it? They simply specify the system they are using in a given document. Doesn't cause much trouble since the differences in all of the systems is by an angle of 180° or 360°. It just causes sign changes in all formula.