In short

Two words both point back to the subject of the clause. себя́ is the reflexive pronoun “-self” (myself, yourself, himself…); it has no nominative and uses one set of forms for every person. свой is the reflexive-possessive “one’s own”; it agrees like мой and means that the thing belongs to whoever is the subject.

The rule

1. себя́ — the reflexive pronoun. Use it when the object of the verb (or of a preposition) is the same person as the subject. It works for any person — я, ты, он, мы, all use the same forms — and it has no nominative (you can never start a sentence with it).

• Я зна́ю себя́. - I know myself.
• Ты ду́маешь то́лько о себе́. - You think only about yourself.
• Он купи́л себе́ маши́ну. - He bought himself a car.
• Возьми́ де́ньги с собо́й. - Take the money with you.

If the object is a different person, use a normal personal pronoun:

• Он ви́дит себя́ в зе́ркале. - He sees himself. (same person)
• Он ви́дит его́ в зе́ркале. - He sees him (somebody else).

2. свой — the reflexive-possessive pronoun. Grammatically it is a possessive (like мой, твой), but it always means “belonging to the subject of the clause” → “one’s own”. It agrees with the noun it describes in gender, number and case.

• Я люблю́ свою́ рабо́ту. - I love my (own) job.
• Она́ забы́ла свои́ ключи́. - She forgot her (own) keys.
• Мы про́дали свой дом. - We sold our (own) house.

3. The key contrast: свой vs его́ / её / их. In the 3rd person this distinction carries real meaning, because его/её/их do not change for “own”:

• Он взял свою́ кни́гу. - He took his own book.
• Он взял его́ кни́гу. - He took his book (= somebody else’s).
• Анна лю́бит свою́ сестру́. - Anna loves her own sister.
• Анна лю́бит её сестру́. - Anna loves her (= another woman’s) sister.

For я / ты / мы / вы there is no ambiguity, so мой and свой are both possible (Я взял свою́/мою́ кни́гу). With он / она́ / они́, prefer свой whenever the owner is the subject.

4. An infinitive has a subject of its own. After попроси́ть, предложи́ть, посове́товать the doer of the infinitive is usually the person in the accusative or dative, and себя́ / свой point at that person, not at the subject of the main verb:

• Он попроси́л сестру́ рассказа́ть о себе́. - He asked his sister to talk about herself (not about him).
• Учи́тель предложи́л ученика́м прове́рить свои́ отве́ты. - The teacher suggested that the pupils check their own answers.

Forms & patterns

себя́ - one set of forms, no nominative, no plural:

свой - declines exactly like мой / твой (agrees with its noun):

* animate accusative = genitive form (Я ви́жу своего́ бра́та; Я зна́ю свои́х друзе́й).

Examples

Common mistakes

• Я ду́маю о мне -> Я ду́маю о себе́ - when the object is the subject again, use себя́, not a personal pronoun.
• Он лю́бит его́ жену́ (meaning his own) -> Он лю́бит свою́ жену́ - свой = own; его́ would mean another man’s wife.
• Возьми́ де́ньги с тобо́й -> Возьми́ де́ньги с собо́й - “with you/oneself” is always с собо́й, for every person.
• Он купи́л себя́ маши́ну -> Он купи́л себе́ маши́ну - “for himself” is the dative себе́, not the accusative.
• …свой брат живёт здесь (as the subject) -> Его́ брат живёт здесь - свой points back to the subject, so it cannot itself be the subject of the sentence.

Tips

• себя́ never starts a sentence: there is no «себя́ делаю» — the doer is the normal pronoun (я, ты…), and себя́ is the object.
• Learn себе́ (dat.) and собо́й (instr.) as set phrases: купи́ть себе́ (buy oneself), взять с собо́й (take along), дово́лен собо́й (pleased with oneself).
• Quick test for свой: ask “whose? — the subject’s.” If the owner is the one doing the action, use свой; otherwise use его́/её/их.
• The свой-vs-его́ trap lives in the 3rd person. For я/ты/мы/вы both мой and свой are fine, so save your attention for он/она́/они́.