This course covers current topics in Discrete Geometry. The course focuses on algebraic methods in geometric incidence problems, including Kakeya type problems: packing lines in different directions; Szemeredi-Trotter type problems: counting incidences between lines/points/curves etc.; Sylvester-Gallai type problems: finding structure in point sets with many local dependencies (e.g., many collinear triples). Applications in theoretical computer science are also discussed.