One book I read suggested that God himself was Jesus Christ, Who became flesh, and allowed Himself to be crucified. Is this true?
The theory you proposed is false because it contradicts the Scripture's teaching concerning the Godhead and the Son of Man, Jesus Christ. The clear testimony of Scripture is that Jesus Christ was the Son of God (not the Father Himself) and He was sent by the Father to die for the sins of men. Before doubting the truth of the trinity, we must remember the words of Scripture concerning those who deny the three Persons of the Godhead:
We also recommend you read the following explanation of the Trinity.