"The Greek Anthology" ('Gathering of Flowers') is the name given to a collection of about 4500 short Greek poems (called epigrams but usually not epigrammatic) by about 300 composers. To the collection (called 'Stephanus', wreath or garland) made and contributed to by Meleager of Gadara (1st century BCE) was added another by Philippus of Thessalonica (late 1st century CE), a third by Diogenianus (2nd century), and much later a fourth, called the 'Circle', by Agathias of Myrina. These (lost) and others (also lost) were partly incorporated, arranged according to contents, by Constantinus Cephalas (early 10th century?) into fifteen books now preserved in a single manuscript of the Palatine Library at Heidelberg. The grand collection was rearranged and revised by the monk Maximus Planudes (14th century) who also added epigrams lost from Cephalas's compilation.
The fifteen books of the Palatine Anthology are: I, Christian Epigrams; II, Descriptions of Statues; III, Inscriptions in a temple at Cyzicus; IV, Prefaces of Meleager, Philippus, and Agathias; V, Amatory Epigrams; VI, Dedicatory; VII, Sepulchral; VIII, Epigrams of St. Gregory; IX, Declamatory; X, Hortatory and Admonitory; XI, Convivial and Satirical; XII, Strato's 'Musa Puerilis'; XIII, Metrical curiosities; XIV, Problems, Riddles, and Oracles; XV, Miscellanies. Book XVI is the Planudean Appendix: Epigrams on works of art.
Outstanding among the poets are Meleager, Antipater of Sidon, Crinagoras, Palladas, Agathias, Paulus Silentiarius.
The Loeb Classical Library edition is in five volumes. Volume I contains Books I-VI; Volume II, Books VII-VIII; Volume III, Book IX; Volume IV, Books X-XII; Volume V, Books XIII-XVI.
Various is the correct author for any book with multiple unknown authors, and is acceptable for books with multiple known authors, especially if not all are known or the list is very long (over 50).
If an editor is known, however, Various is not necessary. List the name of the editor as the primary author (with role "editor"). Contributing authors' names follow it.
Note: WorldCat is an excellent resource for finding author information and contents of anthologies.
I first discovered the Greek Anthology in 1997, I believe, and was instantly enchanted with certain selections (such as the book of Amatory Epigrams). Others seem kind of boring (inscriptions on dedications and churches? really?), but the gems more than make up for the dross. And it *is* neatly separated out into books of differing themes, after all.