This three volume set was used in my introductory Chinese (Mandarin) class in college, along with the accompanying Chinese Character Text. It utilizes Pinyin romanization, in which diacritical marks are used to indicate the four tones, as opposed to the GR system (also available from PUP). The three volumes are as follows:
Chinese Primer: Lessons, (Blue Book), which contains thirty-seven lessons, divided into thematic sections, from the introductory "Foundation Work," which includes five lessons on such topics as tones, initials & finals, and pinyin romanization; and eight Units, devoted to subjects ranging from "Students" to "Dogged Localizers and Directional Complements."
Chinese Primer: Notes and Exercises, (Red Book), which contains vocabulary, grammatical and cultural notes, and exercises corresponding to each lesson in the Blue Book, starting with Unit 1, Lesson 1.
Chinese Primer: Character Workbook, (Yellow Book), which introduces the student to the characters themselves. Each page contains five characters, along with their Pinyin romanization, English meaning, the radical of the character, and the number of strokes used in the character (in addition to the radical). This last is important, as the Chinese writing system is not an alphabet, and dictionaries are organized by stroke number.
It has been some time since I took this class, but I recall finding this system a comprehensible and organized method of learning a complex language that is quite dissimilar to English. If the student follows the recommendation of learning five characters a day, studies regularly, and pairs this set with a good recording, I think they have an excellent chance of succeeding in their first year of Chinese study.
I should note that the characters used are traditional, as opposed to the simplified characters currently in use in the People's Republic. I've always found it somewhat ironic that almost all Chinese-language publications in the United States are printed using the traditional characters, whereas almost all collegiate instruction, geared toward study abroad and interaction with Beijing, utilizes the simplified characters after the first year.