These notes were created by Marta Cristina Pereyra for the short course Wavelets: Theory and Applications,
at the I Panamerican Advanced Studies Institute in Computational Science and Engineering (PASI), Universidad Nacional de Chordoba, Chordoba, Argentina, June 24{July 5, 2002. They were modied and extended by Martin J. Mohlenkamp for the short course Wavelets and Partial Differential Equations, at the II Panamerican Advanced Studies Institute in Computational Science and Engineering, Universidad Nacional Authonoma de Honduras, Tegucigalpa, Honduras, June 14{18, 2004. These courses are similar but not identical, so the notes do not exactly represent either course. We would like to thank the organizers for the invitations to participate in these institutes. We hope that these notes will help you to begin your adventures with wavelets.