The Enterprise and Desktop Search problems recently received a considerable amount of attention from academia, mainly due to the increasing demand in industrial solutions supporting various search tasks in intranets. While challenges arising in intranet search are not entirely new comparing to those that web community has faced for years, advanced web search technologies are often unable to address them properly. In this course we give research prospective on distinctive features of both Enterprise and Desktop Search, typical search scenarios, existing ranking techniques and algorithms. First lecture gives a general introduction, reviews existing systems and outlines typical research challenges. In our next lecture we plan to summarize advanced ranking algorithms and personalization methods utilizing implicit and explicit feedback from users. Third lecture provides an overview of exploratory search methods, including search result clustering/ categorization, faceted search, as well as related techniques stimulating interaction with a user. Later, we discuss latest developments in expert/people search, for example, graph-based and language model based methods. Last lecture covers various aspects of Desktop search: state-of-the-art research prototypes, advanced real-world applications and recent break-through ideas like just-in-time retrieval and task context detection. The course is wrapped up with discussion on open problems and research directions in Enterprise and Desktop search.