Usages
2 distinct jobs 所 does in the Analects, each with examples from the text.
1That which (所 + verb)
Placed before a verb, it names the object of that verb rather than its agent. 所好 is not "the one who likes" but "what is liked".
仲弓問仁。子曰：「出門如見大賓，使民如承大祭。己所不欲，勿施於人。在邦無怨，在家無怨。」仲弓曰：「雍雖不敏，請事斯語矣。」
Zhonggong asked about perfect virtue. The Master said: "It is, when you go abroad, to behave to every one as if you were receiving a great guest; to employ the people as if you were assisting at a great sacrifice; not to do to others as you would not wish done to yourself; to have no murmuring against you in the country, and none in the family." Zhonggong said: "Though I am deficient in intelligence and vigor, I will make it my business to practice this lesson."
Legge 1861
所不欲 = the thing not wanted. Contrast 者, which would give "one who does not want".
子曰：「富而可求也，雖執鞭之士，吾亦為之。如不可求，從吾所好。」
The Master said, "If it were appropriate to seek wealth, even if it meant working as a guard holding a whip, I'd still do so. Since it's not, instead I'll pursue my own passions."
Editor's translation
Read the commentary
吾所好 = that which I love — the object, not the lover.
子曰：「君子無所爭，必也射乎！揖讓而升，下而飲，其爭也君子。」
The Master said: "The student of virtue has no contentions. If it be said he cannot avoid them, shall this be in archery? But he bows complaisantly to his competitors; thus he ascends the hall, descends, and exacts the forfeit of drinking. In his contention, he is still the junzi."
Legge 1861
無所 + verb = there is nothing that.
子曰：「吾自衛反魯，然後樂正，雅頌各得其所。」
The Master said: "I returned from Wei to Lu, and then the music was reformed, and the odes of the royal songs and praise songs all found their proper places."
Legge 1861
所 as a plain noun, "place".
2The means by which (所以)
With 以 it names the instrument or reason: the thing by means of which something happens.
子曰：「不患無位，患所以立；不患莫己知，求為可知也。」
The Master said: "A man should say, 'I am not concerned that I have no place, I am concerned how I may fit myself for one. I am not concerned that I am not known, I seek to be worthy to be known.'"
Legge 1861
所以 gives the ground of the action.
子曰：「視其所以，觀其所由，察其所安。人焉廋哉？人焉廋哉？」
The Master said: "See what a man does. Mark his motives. Examine in what things he rests. How can a man conceal his character? How can a man conceal his character?"
Legge 1861
所以 = that whereby.
子曰：「吾之於人也，誰毀誰譽？如有所譽者，其有所試矣。斯民也，三代之所以直道而行也。」
The Master said: "In my dealings with men, whom do I overpraise, and whom do I unjustly depreciate? If there be some that I overpraise, there must be something in them on which I have, as it were, made trial. This people of the present day! — they are the same that the three dynasties were kept in their straight path by."
Legge 1861
The fullest 所以 in the text.
Combos
2 fixed patterns built on 所, with the role each plays and where to read them.
"The reason why..." / "That by which..."
Can mean either "the reason" or "the means by which." Context determines meaning.
"Have nowhere to..." / "Have nothing to..."
Indicates lack of object or target for action.