In the project we have investigated a broad spectrum of fundamental optimization problems. We examined classical scheduling problems, such as makespan minimization, as well as basic packing problems, such as knapsack and bin packing. We have also considered essential selection problems, including the secretary problem. Additionally, our research has addressed central resource management and data structuring problems. For each of these settings, we have developed new and significantly improved performance guarantees. In some cases, we were able to provide the first progress after 25 years. Our results rely on new algorithms, input models and analysis techniques. In the area of graphs algorithms, we have explored fundamental online matching and graph coloring problems. We have studied the value of randomizing and settled the performance of the most popular and widely used strategies. In the project we have also investigated various problems in the area of energy-efficient algorithms. In particular, we have conducted the first comprehensive algorithmic study of energy conservation in data centers. Finally, our project work has addressed time-inconsistent planning, a modern problem at the interface of computer science and behavioral economics. We have settled the computational complexity and approximability of basic problems. Moreover, we have introduced novel performance measures and related their expressiveness.