What are Tybalt's motives in act 3 scene 1, and what does he hope to accomplish?Romeo and Juliet by William Shakespeare

Tybalt is part of the younger generation of Capulets to
continue the feud which has gone on for years and years.  Incited by the opening street
confrontation between the two families, Tybalt is further angered when he learns that
Romeo and friends have come uninvited for his close cousin,
Juliet.

Now, in Act III Tybalt wants to know why Romeo was
at the party and ascertain his motives, so he calls out in a taunting manner to
Mercutio

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Mercutio, thou consort'st with
Romeo--

When Romeo does
arrive, Tybalt insults him,

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Romeo, the hate I bear thee can
afford

No better term than this--thou art a villain.
(III,i,50)

Tyblat further
tells Romeo that he has caused him "injuries," and challenges him to a duel. For, the
effrontery that Romeo and his friends have displayed by coming to their enemy's house
uninvited is considered a grave insult to the Capulet name.  In the Italy of the
fourteenth century, family name and its honor were of paramount
importance.