Possessive adjectives
Possessives say who owns something: my, your, his, our. In Spanish they go before the noun, and most forms only change with number, not gender. The exceptions are 'our' and 'your' (vuestro), which also show gender.
The full table
mi (my) → mis (my, plural). tu (your, informal) → tus — no accent mark, don't confuse with tú (the pronoun). su (his/her/their/your formal) → sus. nuestro/nuestra (our) → nuestros/nuestras. vuestro/vuestra (your, plural informal — Spain only) → vuestros/vuestras. su/sus also covers 'your' for ustedes.
Agreement with what's owned
mi and tu don't show gender — only number: mi gato, mi casa, mis gatos, mis casas. nuestro shows both gender and number, because it agrees with the noun: nuestro gato (our cat), nuestra casa (our house), nuestros gatos, nuestras casas.
The catch-all 'su'
su works for él, ella, usted, ellos, ellas, ustedes — meaning it can be 'his', 'her', 'their', or 'your' (formal). Context usually makes it clear. To clarify, you can say: el coche de él (his car), el coche de ellos (their car) — literally 'the car of him'.
Where the possessive sits
Right before the noun, no article: mi amigo (not 'el mi amigo'). If there's an adjective, it goes after: mi amigo nuevo (my new friend).
