I—Lattice Paths and Combinatorial Methods.- 1 Lattice Paths and Faber Polynomials.- 2 Lattice Path Enumeration and Umbral Calculus.- 3 The Enumeration of Lattice Paths With Respect to Their Number of Turns.- 4 Lattice Path Counting Simple Random Walk Statistics, and Randomizations: An Analytic Approach.- 5 Combinatorial Identities: A Generalization of Dougall’s Identity.- 6 A Comparison of Two Methods for Random Labelling of Balls by Vectors of Integers.- II—Applications to Probability Problems.- 7 On the Ballot Theorems.- 8 Some Results for Two-Dimensional Random Walk.- 9 Random Walks on SL(2, F2) and Jacobi Symbols of Quadratic Residues.- 10 Rank Order Statistics Related to a Generalized Random Walk.- 11 On a Subset Sum Algorithm and Its Probabilistic and Other Applications.- 12 I and J Polynomials in a Potpourri of Probability Problems.- 13 Stirling Numbers and Records.- III—Applications to Urn Models.- 14 Advances in Urn Models During The Past Two Decades.- 15 A Unified Derivation of Occupancy and Sequential Occupancy Distributions.- 16 Moments Binomial Moments and Combinatorics.- IV—Applications to Queueing Theory.- 17 Nonintersecting Paths and Applications to Queueing Theory.- 18 Transient Busy Period Analysis of Initially Non-Empty M/G/l Queues—Lattice Path Approach.- 19 Single Server Queueing System with Poisson Input: A Review of Some Recent Developments.- 20 Recent Advances in the Analysis of Polling Systems.- V—Applications to Waiting Time Problems.- 21 Waiting Times and Number of Appearances of Events in a Sequence of Discrete Random Variables.- 22 On Sooner and Later Problems Between Success and Failure Runs.- 23 Distributions of Numbers of Success-Runs Until the First Consecutive k Successes in Higher Order Markov Dependent Trials.- 24 OnMultivariate Distributions of Various Orders Obtained by Waiting for the r-th Success Run of Length k in Trials With Multiple Outcomes.- 25 A Multivariate Negative Binomial Distribution of Order k Arising When Success Runs are Allowed to Overlap.- VI—Applications to Distribution Theory.- 26 The Joint Energy Distributions of the Bose-Einstein and of the Fermi-Dirac Particles.- 27 On Modified g-Bessel Functions and Some Statistical Applications.- 28 A g-Logarithmic Distribution.- 29 Bernoulli Learning Models: Uppuluri Numbers.- VII—Applications to Nonparametric Statistics.- 30 Linear Nonparametric Tests Against Restricted Alternatives: The Simple-Tree Order and The Simple Order.- 31 Nonparametric Estimation of the Ratio of Variance Components.- 32 Limit Theorems for M-Processes Via Rank Statistics Processes.- Author Index.