Written initially for a part of a differential geometry class I was teaching, this monograph uses maps and flows to introduce some ideas in geometric analysis. When I first completed them, I declared them to be Version 0.9 and handed them out to current and former students plus probably 20-30 other people. One person, a former student on mine and Matt Sottile’s, Altaa Tumurbaatar, read all the notes carefully and handed them back with errata highlighted and comments on explanations. Thanks to this feedback, I was able to correct a number of errors and typos and version 1.0, became available. Feel free to download, to print, but not to modify, create derivative works with, etc. under the Creative Commons License CC BY-NC-ND 4.0.