Abraham Millgram, Jewish Worship (Jewish
Publication Society, 1971)
Probably the best treatment. Unfortunately out of print, but there are copies
around.
Evelyn Garfiel, Service of the Heart (Burning Bush Press, 1958)
Hayim Donin, To Pray as a Jew (Basic
Books, 1980)
Extensive treatment of rules and practices, from a rather narrow Orthodox viewpoint.
Barry Holtz, ed., Back to the Sources: Reading the Classic Jewish Texts, Chapter 8 “Prayer and the Prayerbook” by Alan Mintz (Summit Books, 1984)
Richard Siegel, Michael Strassfeld, and Sharon
Strassfeld, eds. The First Jewish Catalog (Jewish Publication Society, 19??)
Good section on prayer and services. Still in print.
Kol Haneshamah (Reconstructionist Press,
199?)
The new Reconstructionist siddur, with interesting notes and commentary.
The Metsudah Siddur (Ziontalis, 1963)
Traditional siddur, with line-by-line, fairly literal translation. The Sabbath/Festival
edition is out of print, but the available daily edition includes the Shabbat
and holiday liturgy.
Joseph H. Hertz, ed., Daily Prayer Book
(Bloch, 1959)
Contains extensive commentary, by the same Chief Rabbi of Britain who produced
the “Hertz Chumash”.
Babylonian Talmud, tractace Brachot
The basic source about the Shma, Amidah, Birkat haMazon, blessings for various
occasions.
Judith Z. Abrams, The Talmud for Beginners,
Volume I:Prayer (Jason Aronson, 1991)
An introduction the material in the Talmud (Brachot) on prayer. She discusses
prayer as about relationship.
Joseph Heinemann, Prayer in the Talmud: Forms
and Patterns (de Gruyter, 1977)
Very scholarly. Originally written in Hebrew, I think.
Max Arzt, Justice and Mercy: Commentary on
the Liturgy of the New Year and the Day of Atonement (Holt, Rinehart and
Winston, 1963)
On the High Holiday liturgy, but with good discussions of the parts that are
not specific to those days, including the Shma and Amidah.