This course offers a brief introduction to matrix-analytic methods and their applications in queueing theory, inventory theory, supply chain management, telecommunications networks, reliability, finance mathematics, risk and insurance analysis, and biostatistics. In the first half of the course, the basic theory on phase-type distributions, Markovian arrival processes, and matrix-geometric solutions is introduced. In the second half of the course, applications of matrix-analytic methods in stochastic modeling (queueing, reliability, inventory, supply chain, etc.) are examined.