In the Software Debugging course on Udacity, students will learn about the theory and application of debugging, including the scientific method and its relevance to debugging. They will also explore the history of computer science, including the first bug ever recorded. Through practice exercises, students will build a simple tracer and improve upon it, as well as learn about assertions in testing and debugging, including the most expensive bug in history. They will also delve into strategies for simplifying failures, such as binary search and the delta debugging principle, and participate in a Mozilla bugathon. The course will cover the cause-effect chain, deduction, dependencies, and slices, with a fun fact relating to Sherlock Holmes and Doctor Watson. Students will improve their delta debugger and learn about different types of bugs and the systematic reproduction process. They will also explore bug database management, classifying bugs, bug maps, and learning from mistakes, with a fun fact about a programmer with the most buggy code. Finally, students will have the opportunity to improve their tools and practice on a real-world bug database.