In the first part "Mechanism Design and Monotone Algorithms", the motivating question is whether the results on truthful mechanisms in Archer and Tardos'' paper "Truthful Mechanisms for One-Parameter Agents" are basically a rediscovery of those Myerson introduces in his paper "Optimal Auction Design". To answer that question, we reveal similarities and differences of both papers and give alternative proofs of the main result to underline the correlation of the approaches. The first part also provides the background for the second part "Bounds for Monotone Scheduling Algorithms". Here, we consider monotone algorithms in the context of scheduling problems. We develop a general model to find lower bounds for a certain scheduling problem. In a related matter, we classify monotone algorithms for the deterministic, randomized and online case and prove lower bounds for these algorithms.