The golden rule is, finish it first! And makes sure it’s really ready. Check out our guidelines on how to approach a publisher.
Even if you a publisher only wants to see the first three chapters, you must have completed the entire manuscript before approaching the publisher. If they read three chapters and like it, they will ask for more – making them wait can be a good way to lose their interest.
Publishers will sometimes accept unfinished manuscripts for non-fiction, but this is usually only for writers with whom they already have a relationship.