Counterinsurgency (COIN) has been a hot topic over the past decade with the US-led coalition wars in Iraq and Afghanistan. If you are new to the topic, there is an endless stream of commentary and analysis on the topic, so it can be overwhelming trying to figure out where to start. In addition, FM 3-24 (PDF) is lengthy and about to be replaced.
These online articles are the perfect spot to begin.
Two Schools of Classical Counterinsurgency (2007) by Dave Kilcullen — In this article, Kilcullen talks about the enemy-centric and population-centric approaches of classical counterinsurgency, which will be two terms you will see a lot throughout COIN writings.
In this work, Thinking and Writing About COIN (2013) by John T. Fishel and Edwin G. Corr, the authors give a book review of Fred Kaplan’s The Insurgents: David Petraeus and the Plot to Change the American Way of War. However, the useful aspect is the lengthy historiography of COIN literature and influence over the past 100 years. Some of the names will likely be familiar (e.g., Sun Tzu, Mao) while others may be more obscure. Still, someone jumping into learning about counterinsurgency will benefit from the list for further reading.