The preposition con means a company:
Voy al cine con mi novio = I go to the cinema with my boyfriend
It is also used with some emotion states:
Estoy contento con mis hijos – I am glad with my children
Estoy enfadada con mi novio – I am angry with my boyfriend
Con las palabras yo, tú forma palabras conmigo, contigo:
Voy al cine contigo = I will go to the cinema with you
¿Estás enfadado conmigo? – Are you angry with me?
The form conmigo is often used with the verb venir in order to invite somebody:
¿Vienes conmigo a comer? – Will you come with me to have a lunch?