Spatial audio is a set of techniques that aims to simulate sound sources located in a specific position of space. This is achieved thanks to the Head-Related Transfer Functions (HRTFs) that model the anatomical characteristics of a person and their interaction with the incident sound field. This project presents a study on the analysis and synthesis of HRTFs through Principal Component Analysis (PCA). We explain in detail the analysis and synthesis procedures carried out during this project. In the analysis stage, we determine the number of principal components that preserves 95 % of variance of the high-dimensional HRTFs. Following this, we evaluate the performance in a synthesis stage by reconstructing the HRTFs from their low-dimensional representation. The results obtained show that the azimuth angles are strongly correlated with the principal components of PCA, while the elevation angles are poorly described by them. Lastly, the cross-validation error used in the synthesis shows that there is greater spectral distortion in the listener's ipsilateral. Finally, and considering the spectral distortion obtained in the synthesis, we conclude that PCA correctly captures relevant information from the HRTFs.