Nostr: Can I run my own Nostr relay?

Short answer

Yes. A relay is server software that accepts, stores, and serves Nostr events over the protocol. Running one means choosing storage, moderation, access rules, backups, updates, and an uptime plan. NIP-11 lets a relay advertise its capabilities and policies to clients. A personal relay can give you more control over your copy of events, but other users still need a way to discover it.

Sources

NIP-01: Basic protocol, NIP-11: Relay metadata.