Schaff, Philip. History of the Christian Church (The Complete Eight Volumes in One). Amazon Kindle Edition, 2014.
Volume 2, Ante-Nicene Christianity A.D. 100-325, “Chapter 5. Christian Worship” (Includes an introduction and sections 59-74).
§66. Parts of Worship.
A discussion of the seasons of the church year rather naturally leads to a consideration of the actual elements of a worship gathering. Readings of the Old Testament were present from the earliest days, as they were already the norm in the synagogue. As instruction moved away from apostolic orality, the reading of parts of the New Testament was regularly added (Schaff 2014, Loc. 15100). At times, readings which never became canonical were used as well. Meetings typically contained a sermon, an exhortation or exposition based on Scripture. By the mid second century it is clear that the sermon was delivered by an elder, and preferably a bishop (Schaff 2014, Loc. 15112). Prayers were normally carefully composed, including quotations from the Old Testament. These are recorded as early as the close of the first century (Schaff 2014, Loc. 15118). Singing of the Psalms was adopted directly from the synagogue (Schaff 2014, Loc. 15125). It seems clear that early Christians also composed their own songs. Schaff includes samples, then a copy of a prayer from Clement of Rome (Schaff 2014, Loc. 15149). Schaff observes that these ancient prayers have frequently inspired more recent church music (Schaff 2014, Loc. 15191).