Using trajectory inference methods, a dynamic differentiation process can be inferred from one single-cell transcriptomics experiment. We aim to improve trajectory inference to more robustly and accurately determine the biological trajectory present, and to allow a more fine-grained view into the differences between cells in their differentiation process. A drawback to widespread adoption of trajectory analysis is the effort required to extract a correct biologically meaningful trajectory. Often, multiple methods need to be tried out and a variety of parameters adjusted. I will combine multiple methods to increase the probability of finding an accurate consensus trajectory. Comparing multiple complex trajectories is not possible with the current methods. In this project I will develop new methods that can align more than two non-linear trajectories. I will also set up a benchmarking platform, integrating a variety of performance measures and multiple simulated and publicly available datasets, to validate methods for trajectory alignment. These methods will be used to align differentiation trajectories present in normal and abnormal development of intestinal stem cells in the crypts of the colon niche using samples from patients with colon cancer, and of B and T cells present in SARS-Cov-2 positive and negative patients in PBMC and airway wash (BAL) samples.