This series of four lectures will provide an introduction to multidimensional conservation laws, along with a perspective on a list of open problems. The main topics will include: Prototypes and Basic Features/Phenomena Multidimensional Models Multidimensional Steady Problems Multidimensional Self-Similar Problems Compressible Vortex Sheets and Related Problems Divergence-Measure Fields and Hyperbolic Conservation Laws Lecture References: Gui-Qiang Chen, Euler Equations and Related Hyperbolic Conservation Laws, In: Handbook of Differential Equations: Evolutionary Differential Equations, Vol. 2, pp. 1-104, 2005, Eds. C.~M. Dafermos and E. Feireisl, Elsevier: Amsterdam, Netherlands Gui-Qiang Chen and Mikhail Feldman, Shock Reflection-Diffraction and Multidimensional Conservation Laws, In: Proceedings of the 2008 Hyperbolic Conference: Theory, Numerics, and Application, AMS: Providence, 2009. Gui-Qiang Chen, Monica Torres, and William Ziemer, Measure-Theoretical Analysis and Nonlinear Conservation Laws, Pure Appl. Math. Quarterly, 3 (2007), 841-879 (To Leon Simon on his 60th birthday). Gui-Qiang Chen, Marshall Slemrod, and Dehua Wang, Conservation Laws: Transonic Flow and Differential Geometry, In: Proceedings of the 2008 Hyperbolic Conference: Theory, Numerics, and Application, AMS: Providence, 2009. *You may directly download them from http://www.math.northwestern.edu/~gqchen/preprints/