You can't talk about social structure in Rome without talking about the Roman family. Legally, in Rome, people were not treated as individuals, but as family groups. The paterfamilias (the oldest male member of the family--father or grandfather), controlled all the assets of all of the family, even of grown sons and grandsons (male heirs). He could choose whether each child born in the family was kept or abandoned to die. He was held responsible if one of the members of his family committed a crime. When the paterfamilias died, men who lived in their own households at the time of the pater's death became the paterfamilias of those households.
Women had a choice when they married to remain financially under their “pater” or transfer control to their husband. Most choose the former, since it gave them some financial freedom from their spouse, and a chance of a future inheritance of their own. Even so, Roman law required that a women have a male guardian of some sort until she had born three children (four for freedwomen). During the empire women could replace their guardians at will.
Social Class in Rome
Roman social class was written into Roman Law, and affected all areas of life. Your social class defined everything from who you could marry, where you sat at a theater, and what quality of food and wine you might be served at a dinner party.
Though the 900 members of the senate were the most powerful class under the Emperor. Membership in the Senate was generally limited to those those with a pedigree of distinguished ancestors and considerable wealth (one million sesterces to be exact). Senators were prohibited from engaging personally in non-agricultural business, trade or public contracts. They wore a toga with a dark purple trim.
Those who could claim two generations of free birth and possessed 400,000 sesterces could become an Equestrian (and Equestrians who fell short of that amount of wealth lost the status). Unlike senators, Equestrians were allowed "unlimited participation in commerce, trading, and governmental contracts," though they often choose to rest on their wealth and land-holdings and not engage in business.
Common Citizens (Plebeians)
The common citizen class included both those who were quite well off to the poorest of the poor. Citizens were allowed to wear the white toga.
Some freed slaves received rights similar to those of citizens, while others were treated legally more like foreigners, depending the manner in which they were free. There were ways for some slaves to receive full rights as citizens (such as serving 6 years at a Vigeles, or Roman Firefighter). Freed slaves still had some obligations to their former masters. Children born after they had been freed became full citizens.
Between 25 to 40 percent of the Roman population were slaves, whose work ranged from hard labor, menial work,, work as skilled tradesman, and even managers and teachers. Not all slave masters were servants of the upper class--many were employed by merchants in their businesses. Private slaves had no rights, and their masters could subject them to whatever abuse they wanted (though treating your slaves cruelly was frowned on, so there was some social ramifications to abusing a slave even if there were no legal ones). Slaves were also employed by the government both for public building projects and administrative work. Some higher level government positions for educated slaves even included a salary, and some legal rights that private slaves didn’t have.
All other freeborn people who lived in Rome. They had less rights and privileges than Roman Citizens.
My Sources for the Roman Families
And For Slavery Speicifically
Pictures from Vroma.org