I am going to use this blog to record some of my mathematical thoughts. Modern mathematics has a pretty steep learning curve and I don't really want to spend my time writing about the *basics*. What are the *basics*? I could say something like *everything you learn in a standard mathematics undergraduate degree*, but that is vague. On this site we shall use the following convention: *basic* mathematics is the material contained in the Appendices of Introduction to Smooth Manifolds by John M Lee. I don't have any strong opinions about the book as a whole, but the Appendices line up closely with what I would call *basic* mathematics and they are very well organized. From these *basics*, you can develop a lot of interesting mathematics in a relatively short time period.