Paul, an apostle of Jesus Christ by the will of God, and Timothy our brother, unto the church of God which is at Corinth, with all the saints which are in all Achaia:
Timothy our brother - perhaps Paul's amanuensis of this letter. When writing to Timothy himself, he calls him "my son" (1 Timothy 1:18); writing of him, "brother," etc., and "my beloved son" (1 Corinthians 4:17). He had been sent before to Macedonia, and met Paul at Philippi, when the apostle passed over from Troas to Macedonia (cf. 2 Corinthians 2:12-13; notes, 1 Corinthians 16:10-11).
In all Achaia - comprising Hellas and the Peloponnese. The Gentiles and Annaeus Gallio, the proconsul (Acts 18:1-28), strongly testified their disapproval of the accusation brought by the Jews against Paul. Hence, the apostle was enabled to labour in the whole province of Achaia with such success as to establish several churches (1 Thessalonians 1:8; 2 Thessalonians 1:4), where, writing from Corinth, he speaks of the "churches" - namely, the Corinthian and others also-Athens, Cenchrea, etc. He addresses 'the church in Corinth' directly, and all "the saints" in the province indirectly. In Galatians 1:2 all the "churches" are addressed directly in the same circular letter. Hence, here he does not say, all the churches, but "all the saints."