Acts 18:8

And Crispus, the chief ruler of the synagogue
This was a Jewish name; frequent mention is made of R. Crispa in the Jewish writings ^F11 this person, either through hearing Paul before he departed from the synagogue, or when in Justus's house, which was hard by the synagogue, believed on the Lord with all his house: he believed the doctrine the apostle preached, concerning Jesus, and that he was the Messiah; and he believed in him for life and salvation, and made a profession of his faith in him, and so did all his family, upon which he was baptized by the apostle; see ( 1 Corinthians 1:14 )

and many of the Corinthians hearing
not "his faith", as the Arabic version adds; as if hearing of the faith of Crispus induced them to believe also; for the ruler of the Jewish synagogue had no such influence on the Gentile Corinthians, as these were: but these hearing the Gospel preached by the apostle, very likely in the house of Justus, to which they came,

believed;
faith came by hearing; they believed the Gospel, and they believed in Christ, the sum and substance of it; and not with a bare historical faith, but with a spiritual and saving one, or such as is unto salvation, with their heart, and with their mouth made confession of it:

and were baptized;
not by the apostle, for he baptized at Corinth none but Crispus and Gaius, and the household of Stephanas, but by some of his companions, as Silas, or Timothy, or both: this is a plain instance of believers' baptism; first they heard the word of God; then they believed, this word coming with power to them; and upon their believing, they are baptized. These laid the foundation of a famous church in this place, which continued for many ages after; Silas, who is reckoned among the seventy disciples, is said to be the first bishop or pastor of it; (See Gill on Luke 10:1); in the "second" century Primus was bishop of this church, with whom Egesippus as he went to Rome stayed some days, and was much refreshed with the orthodox faith of him, and the Corinthians; in the same century Dionysius presided over this church, who was not only very useful to the church under his care, but to many others {l}; in the same age, under Severus lived Bacchylus bishop of Corinth, who wrote a book concerning Easter in the name of all the bishops in Achaia ^F13; in the third century Tertullian ^F14 makes mention of a church at Corinth; in the fourth century Epictetus was bishop of the said church, and was contemporary and familiar with Athanasius, to whom a letter is extant in the works of Athanasius {o}; in the "fifth" century there was a church at Corinth, and a bishop of it was in the synod at Chalcedon, and it was then a metropolitan church; in this age Peregrinus bishop of Corinth was in the first synod at Ephesus, held against Nestorius, and Erisistratus, a bishop also of the same church, was in another synod at the same place, and Peter bishop of Corinth was in the Chalcedon council; in the "sixth" century mention is made of a bishop of the Corinthians, in the fifth synod at Constantinople, and in the same century Gregory instructed John bishop of the Corinthians rightly to govern the Lord's flock, and exhorted all the Corinthian bishops to concord. In this age Adrianus also was bishop of Corinth, he flourished under Mauritius the emperor; as likewise did Anastasius archbishop of the Corinthians; and he being removed from his office, John succeeded him in it; in the "seventh" century there was a Corinthian bishop in the sixth council at Constantinople ^F16; thus far this ancient church is to be traced in history.