I am reading Moser's paper [*On commuting circle mappings and simultaneous Diophantine approximations*](http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002437821) and I found it hard because it is my first time that I seriously have to read a paper. Could one help me by telling me what are the steps in the proof of the main theorem (Theorem 1), and point out the main ideas he used in the paper. Thank you a lot.