Latent fingerprint recognition involves acquisition and comparison of latent fingerprints with an exemplar gallery of fingerprints. The diversity in the type of surface leads to different procedures to recover the latent fingerprint. The appearance of latent fingerprints vary significantly due to the development techniques, leading to large intra-class variation. Due to lack of large datasets acquired using multiple mechanisms and surfaces, existing algorithms for latent fingerprint enhancement and comparison may perform poorly. In this study, we propose a Multi-Surface Multi-Technique (MUST) Latent Fingerprint Database. The database consists of more than 16,000 latent fingerprint impressions from 120 unique classes (120 fingers from 12 participants). Including corresponding exemplar fingerprints (livescan and rolled) and extended gallery, the dataset has nearly 21,000 impressions. It has latent fingerprints acquired under 35 different scenarios and additional four subsets of exemplar prints captured using live scan sensor and inked-rolled prints. With 39 different subsets, the database illustrates intra-class variations in latent fingerprints. The database has a potential usage towards building robust algorithms for latent fingerprint enhancement, segmentation, comparison, and multi-task learning. We also provide annotations for manually marked minutiae, acquisition Pixel Per Inch (PPI), and semantic segmentation masks. We also present the experimental protocol and the baseline results for the proposed dataset. The availability of the proposed database can encourage research in handling intra-class variation in latent fingerprint recognition.