This thesis presents "cache-oblivious" algorithms that use asymptotically optimal amounts of work, and move data asymptotically optimally among multiple levels of cache. An algorithm is cache oblivious if no program variables dependent on hardware configuration parameters, such as cache size and cache-line length need to be tuned to minimize the number of cache misses. We show that the ordinary algorithms for matrix transposition, matrix multiplication, sorting, and Jacobi-style multipass filtering are not cache optimal. We present algorithms for rectangular matrix transposition, FFT, sorting, and multipass filters, which are asymptotically optimal on computers with multiple levels of caches. For a cache with size Z and cache-line length L, where Z =# (L 2 ), the number of cache misses for an m × n matrix transpose is #(1 + mn=L). The number of cache misses for either an n-point FFT or the sorting of n numbers is #(1 + (n=L)(1 + log Z n)). The cache complexity of computing n ...