Hume's Problems with Induction is intended to describe and refute some of the main doubts and objections David Hume raised with regard to inductive reasoning. It replaces the so-called problem of induction with a principle of induction. David Hume's notorious skepticism was based on errors of observation and reasoning, with regard to induction, causation, necessity, the self and freewill. These are here pointed out and critically analyzed in detail - and more accurate and logical theories are proposed. The present work also includes refutations of Hempel's and Goodman's alleged paradoxes of induction.