This chapter explores three kinds of unsupervised task: clustering, density estimation and dimensionality reduction. Cluster analysis aims to group similar observations together. The K-means algorithm does this by repeatedly reassigning each point to the nearest cluster centre, reducing or maintaining the clustering inertia at each step. Density estimation involves learning a probabilistic model of a data-generating process. Gaussian mixture models represent the distribution as a weighted sum of multivariate normal components. The EM algorithm fits these models by alternating between assigning each component a responsibility for each point and updating component locations using responsibility-weighted averages. Cross-entropy measures how well an estimated density approximates the true one and is minimised when the two match. Dimensionality reduction compresses data into a lower-dimensional latent space via an encoder, with a decoder reconstructing the original data. Principal component analysis uses linear encoder–decoder pairs to minimise reconstruction error, offering a simple yet powerful form of dimensionality reduction.