Seeing the rain come on, we took shelter.
This sentence looks like a complex sentence with a main and an independent clause. But the book says it is a simple sentence. Which is correct?
The introductory phrase Seeing the rain come on is not a clause because it contains no subject-verb relationship. It is a so-called participial phrase.
Hence, we have only one independent clause and no dependent clauses. Your sentence, therefore, is simple.