Complete vector database course: from embedding mathematics and similarity search to production deployment. Pinecone, Weaviate, Milvus, Qdrant, pgvector, Chroma, LanceDB — comparative analysis. ANN algorithms (HNSW, IVF, PQ, DiskANN), hybrid search (vector + BM25), multi-tenancy and partition keys, scaling (sharding, replication), managed vs self-hosted economics, RAG pipeline integration with LangChain/LlamaIndex. Every module contains comparison tables and working code.