Here you can find the lecture notes "Laplacian Matrix for Dimensionality Reduction and Clustering" by Prof. Dr. Laurenz Wiskott from the Institute of Neuroinformatics at Ruhr-Universität Bochum. Another version can be found on the arXiv: https://arxiv.org/abs/1909.08381.

Many problems in machine learning can be expressed by means of a graph with nodes representing training samples and edges representing the relationship between samples in terms of similarity, temporal proximity, or label information. Graphs can in turn be represented by matrices. A special example is the Laplacian matrix, which allows us to assign each node a value that varies only little between strongly connected nodes and more between distant nodes. Such an assignment can be used to extract a useful feature representation, find a good embedding of data in a low dimensional space, or perform clustering on the original samples. In these lecture notes the Laplacian matrix is introduced and then a small number of algorithms presented designed around it.

Furthermore, you can find exercises and solutions to the lecture.