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The "hundred schools" (zhuzi baijia 諸子百家) were thinkers and philosophers of the Spring and Autumn 春秋 (770-5th cent. BCE) and Warring States 戰國 (5th cent.-221 BCE) periods, and in a narrower sense, other than the "Confucians" (rujia 儒家). The predominance of the Confucians (du zun ru shu 獨尊儒術 "only venerate the skills of the Confucians") hailed from Emperor Wu's 漢武帝 (r. 141-87 BCE) decision to "clear up the Six Classics and expel the hundred schools" (biaozhang liujing, bachu baijia 表彰六經，罷黜百家). The idea to "unify all [thought] under Heaven" came from the philosopher Dong Zhongshu 董仲舒 (179-104 BCE), who "Confucianised" the realm of philosophy.
This measure was intended to strengthen the central government by a coherent form of rituals, ceremonies and a metaphysical ideology. The "hundred schools" were not forbidden, as during the time of the First Emperor 秦始皇帝 (r. 246-210 BCE), but Confucian writings were particularly promoted, so the others fell into oblivion, at least for some time. This means that the terms baijia or zhuzi 諸子 "the many masters" did not include Confucian thinking. The word "hundred" just meant, many, and not a specific number.
The term baijia was first used in the book Xunzi 荀子 (ch. Jiebi 解蔽), where it is said that "each of the regional rulers has a different policy, and each of the hundred schools has different [modes of] persuasion (bai jia yi shuo 百家異說)". A chapter (Tianxia 天下) in the book Zhuangzi 莊子 says the writings of the old Classics were often mentioned in the "teachings of the hundred schools" (bai jia zhi xue 百家之學).
Sima Tan 司馬談 (190-110 BCE), the initiator of the universal history Shiji 史記, wrote an essay about the schools of thought. His Lun liujia zhi yaozhi 論六家之要旨 explained the basic ideas, origins and developments of six schools (liujia 六家), namely the "Confucians" (rujia 儒家), Mohists (mojia 墨家), Daoists (daojia 道家), legalists (fajia 法家), dialecticians or "sophists" (mingjia 名家), and the Yin-Yang theoreticians (yinyangjia 陰陽家).
Founded by Confucius, the rujia split up into eight groups, the most famous of which were the schools of Zisi 子思, Meng Ke 孟軻 (Mengzi 孟子) and Master Sun 孫氏 (i.e. Xunzi). The book Hanfeizi 韓非子 (ch. Xianxue 顯學) enumerates the eight Confucian schools as that of Zizhang 子張, Zisi, Master Yan 顏氏 (i.e., Yan Yuan 顏淵), Master Meng 孟氏 (Mengzi), Master Qidiao 漆雕氏, Master Zhongliang 仲良氏, Master Sun (Xunzi), and Master Yuezheng 樂正氏 (Yuezheng Ke 樂正克).
The guidelines of Confucian thought were the veneration of the ancient (mythological) rulers Yao 堯 and Shun 舜, the adherence to the laws of the kings Wen and Wu 文武 of the Zhou dynasty 周 (11th cent.-221 BCE), the observance of rituals and ritual music (li yue 禮樂) and of the virtues kindness and righteousness (ren yi 仁義), the belief in the importance of loyalty and empathy (zhong shu 忠恕), as well as keeping a golden mean (zhongyong 中庸) by respecting social relations (lunli 倫理, education according to the way of virtue (daode 道德, and the application of a policy of paradigmatic virtue (dezhi 德治) and of benevolent government (renzheng 仁政).
The Mohist school, founded by Mozi 墨子, diverged into the teachings of Master Xiangli 相里氏 (or Master Boli 柏夫氏), Master Xiangfu 相夫氏 (or Master Zufu 祖夫氏) and Deng Ling 鄧陵.
The Mohists, occupying the second place in ancient listings, can be called a counterpoint to the Confucians because they held the prodigy of rituals and the lavishness of burials for unnecessary luxury: moderation in funerals (jie zang 節葬) and condemnation of music (fei yue 非樂). Unlike the Confucians, Mohists advocated an all-sided universal love (jian ai 兼愛), and not just one motivated by social relationships. Yet the Mohists, too, refused aggressive war (fei gong 非攻), venerated antiquity (shang xian 尚賢), acknowledged the role of Heaven, but rejected the belief in fate (fei ming 非命). The Mohist branch of sophists was crucial for the development of logic and early natural science.
The Daoists found their origin in Laozi 老子 and later split up into several schools, on the "left" the School of Song [Xing] and Yin [Wen] 宋尹學派, and to the "right" Zhuang Zhou 莊周 (Zhuangzi).
The Daoists believed that humans should not interfere with the natural order of things. The best they could do was seek the original nature of "the Way" (dao 道), which would provide insight into how nature and the entire cosmos function. They promoted a passive way of life (acting through non-action, wu wei 無為) and a cautious approach to governance. Regarding the Confucian models of virtue and social etiquette, Daoists thought that such strict rules contradicted the natural way. They believed humans would not be able to distinguish right from wrong. In this relativistic perspective, Daoists were akin to the sophists or "school of designations" (mingjia), whose members debated the meaningless nature of names and terms. They devised riddles to help see things from different perspectives, so that "identities and differences were again unified" (he tong yi 合同異).
The legalists were divided into the schools of law (fa 法), political skills (shu 術) and royal power (shi 勢).
The legalists, often called "Machiavellists," were supporters of royal authority. In their view, only a written law that was strictly followed could establish order and strengthen the state. While the Confucians governed society through rituals, the legalists governed through law. Laws were applied equally to all members of society. The ruler was backed by means to enhance his personal power and to use his political skills by any means, such as mobilising the peasantry for construction projects and military campaigns. During imperial times, legalist methods were often combined with Confucian principles.
The Yin-Yang school was the oldest of all. It dealt with astronomy, calendar, and astrology. During the Warring States period, Zou Yan 鄒衍 (c. 305-240 BCE) created the theory of the Five Agents (wude zhongshi 五德終始).
Yin-Yang thinkers and the protagonists of the Five Agents believed that the Five Agents influenced the movement of nature, humans, and society. A change between the Agents had to be predicted to bring peace and safety. In politics, the foundation of a new dynasty was seen as a change in agents and had to be accompanied by certain measures linking man, society, the state, and the universe.
Apart from these six schools, there were some others which Han period 漢 (206 BCE-220 CE) theoreticians did not consider as "philosophical". Such were the agronomists (nongjia 農家), storytellers (xiaoshuojia 小說家) and diplomatists or coalition advisors (zonghengjia 縱橫家), as well as "miscellaneous masters" or syncretists (zajia 雜家), whose writings inclined to more than one of the great schools. A singular person, of whom no writings are preserved, was the "hedonist" or "egoist" Yang Zhu 楊朱 (of the "Yang-ist school"). Likewise, not considered schools of their own are the masters of the Jixia Academy in the state of Qi 齊, the Jixia School 稷下學派, and Guan Zhong 管仲 (Guanzi 管子, 725-645 BCE), a politician and theoretician from the same state, with the School of Guan Zhong 管仲學派.
The canonization of the "hundred schools" made a step further in Liu Xin's 劉歆 (46 BCE-23 CE) descriptive bibliography Qilüe 七略 from the late Former Han period 前漢 (206 BCE-8 CE). He discerns ten schools, namely the Confucians, Mohists, Daoists, legalists, Yin-Yang thinkers, sophists, diplomatists, agronomists, miscellaneous masters, and storytellers. His categorisation is preserved in the bibliographical chapter Yiwen zhi 藝文志 of the official dynastic history Hanshu 漢書. In this catalogue, the storytellers were considered as unworthy of being counted among the "masters and philosophers". Confucian writings were included in the "Epitome of the Six Classics" (Liuyi lüe 六藝略), while the other writings were in the "epitome" of the masters (Zhuzi lüe 諸子略).
Quite interesting is the number of books recorded in the bibliography, which amounts to 198 "schools" (jia 家), actually books, with a chapter number of no less than 4,324. Yet this number also includes writings of the very late Warring States and the early Han period, which can actually not be counted among the "hundred schools" of pre-imperial times.
The term zhuzi baijia is also mentioned in Jia Yi's 賈誼 (200-168 BCE) biography (ch. 48 Jia Yi zhuan 賈誼傳) in the Hanshu, where it is said that as a young man, Jia Yi read the "books of the hundred masters" (tong zhuzi baijia zhi shu 通諸子百家之書). This shows that in the second century BCE a kind of canon of "masters" was already available in private or state-owned libraries.