There are different incarnation of the Maslov index. The one that I most prefer is the one propose in Arnold's paper suggested by Igor Rivin. The paper by Cappell-Lee-Miller suggested by Greg Friedman is also an excellent source. (These two papers helped me understand this concept but they addressed primarilty to a mathematical audience.

Maslov introduced his index in his investigation of asymptotics of certain oscillatory appearing in quantization problems. I suspect this is closest to what had in mind. It is sometime known as the Hormander index. Section 3.4 of Duistermaat's book Fourier Integral Operators has a rather efficient description of the Maslov index. As an aside, the operators introduced and investigated by Maslov are special examples of Fourier integral operators.

There are different incarnation of the Maslov index. The one that I prefer is the one proposed in Arnold's paper suggested by Igor Rivin. The paper by Cappell-Lee-Miller suggested by Greg Friedman is also an excellent source. (These two papers helped me understand this concept but they addressed primarilty to a mathematical audience.)

Maslov introduced his index in his investigation of asymptotics of certain oscillatory appearing in quantization problems. I suspect this is closest to what had in mind. It is sometime known as the Hormander index. Section 3.4 of Duistermaat's book Fourier Integral Operators has a rather efficient description of the Maslov index. As an aside, the operators introduced and investigated by Maslov are special examples of Fourier integral operators.