Niddah 45 - Ages of Legal Responsibility
A father has the authority to betroth his daughter when she is a minor. The preferred way is for the girl to grow up and decide on her own, but this legal right gives her father a way to arrange the marriage early, which in view of persecutions and short lifespan was often beneficial. Thus, a minor girl may be legally considered a married woman, even while she continues to live with her family until she grows up.
At the age of three, she creates a legal responsibility for anyone who cohabits with her - he is liable for adultery, although she is not, until she reaches the bat mitzvah age. In the same vein, if her prospective husband dies, his brother has an obligation to take her as a wife, effected as yibum (levirate marriage), and that can happen even when she is a minor. If she does not want him, she can give him a release (halitzah), but only when she is a bat mitzvah.
A boy can effect yibum from the age of nine: if his adult brother, who has the legal capacity to marry a woman, does so, but then dies, then this woman is connected to him because of his older brother, and this connection is what allows him to marry her. However, to receive a halitzah, or to give a Get (divorce), he needs to be a bar mitzvah.
The vows of a girls are binding one year prior to her bat mitzvah, if it is clear that she understands the consequences of her words. For the boy this age starts at one year before bar mitzvah.
Art: Jan Hermansz. van Biljert- The Betrothal - The Groom