This thesis introduces a formal general framework for scaling blockchain protocols by sharding. The framework is modular and it can be adjusted for different needs or sets of assumptions. We prove that sharded protocols obtained by following our scheme (with correct modules in place) live up to the same safety and liveness guarantees as their non-sharded counterparts. The proof is general and relies on well-defined specifications of certain components. This lays the ground for simple proofs of correctness for sharded protocols obtained by following the proposed scheme. The framework is not left as an obscure specification of some high level structure; explicit use is demonstrated by applying it to shard Algorand. As part of this concrete construction, a tamper-proof mechanism to assign nodes to shards is introduced. This mechanism is constructed by using verifiable random functions and can safely withstand a powerful adaptive adversary.