Citizens, and Slaves
The class system in Athens was made up of two distinct classes- slaves and citizens. These classes were rarely open to any of the other classes; citizenship alone was given only to male Athenians. The same hierarchy of classes existed within other Greek city states as well (an even finer division can be drawn when looking at the social structure of Sparta). At the core of each class was a specific list of duties and responsibilities given to a member of it. Thus, citizens were expected to have attended the gymnasium, and palaistrai, where as slaves were relegated to house chores and could never attain citizenship.
Legitimacy and Marriage
During the Classical Age (500 BC - 400 BC) rules for citizenship in Athens were strengthened. This was possibly done to ensure that the essentially Athenian elements of the culture were retained during a time of turmoil, and/ or to discourage mixed marriages. During the Classical Age, conflicts with the Persians became paramount, so much so that by 479 - 480 BC, the Delian League was founded. The Delian League was made up of a counsel from numerous city states who, with combined force took up arms against the Persians and managed to reclaim their former cities. To add to the conflicts within the Classical Age, under the rulership of Pericles, Athens itself was under continual strain. A plague and a revolt continued from 430 - 404 BC, also known as the Peloponnesian war. Athens eventually surrendered to Sparta at the end of the war.
A stricter system of determining citizenship was not amicable to all former Athenian citizens from an earlier era. Many citizens found themselves at a loss of their inheritance, citizenship and family ties. Under Pericles' rule, marriages had to be made through a legally recognized process. This process meant that in order for a marriage to be legal and the resulting children legitimate, both the mother and father had to be Athenians, and in addition the father and mother of the married couple also on both sides, had to be Athenians. The consequences of Pericles' ruling meant many citizens were no longer citizens of Athens. That in turn also meant that many had their inheritance or land taken from them. The stress the citizenship rule had upon Athens rippled through the general populace and was even felt by Pericles. Pericles, who had lost his sons in the Athens plague, was forced to ask permission from the Assembly to admit the children of his Milesian mistress, as Athenian citizens.
Citizens
Citizenship allotted many privileges to the population of Athens, thus it was difficult to attain and was only given to a male child if both parents were Athenian. Women were excluded from becoming citizens (with limited exception in the later Hellenistic period). Hereditary links however, did not just determine citizenship. From the time of their birth, young Athenian men were expected to attain an education. Based upon their birth and the wealth of their parents, the length of education was from the age of 5 to 14; for the wealthier 5 to 18, and sometimes into a students' mid-twenties. Unfortunately the above only applied to the 6th Century BC, when formalized schools were established. By the 4th Century BC in Hellenistic Greece, a potential citizen spent 2 years in the gymnasium, and 2 years training in the military, also known as the ephebeia. Citizens had rights which for the most part were limited only to themselves. Namely, a citizen could own land, have heirs, own slaves, belong to the assembly, and could have some political sway. Citizens also played a large part in the year-round religious festivals of Athens.
Slaves
Citizenship allotted many privileges to the population of Athens, thus it was difficult to attain and was only given to a male child if both parents were Athenian. Slaves alternately were below their citizen titled masters. They were excluded from the religious festivals of Athens, could not own land, were denied some civil rights, could not participate in political activities. They were able to hold dominance over many of the trades. Tradework itself was appalling to most citizens. Slaves were not expected to attain anything but a basic education in Greece, but were not excluded from it. Some masters allowed their younger slaves apprenticeships in their workshops; eventually the slaves wares and income would add to their master's wealth. Some of the wealthier students in the Greek academies brought a slave with them to their classes. Slave work ranged from the light domestic work to the heavy work in the mines of Nubia, and other places. In some cases, domestic slaves were ritually welcomed into the house, by a walk around the hearth, and adoption (prior to Pericle's ruling) was not an unlikelihood with child slaves.
Note: (Some scholars denote a third class of Foreigners. The basic role in Greek society of a foreigner was for trade and wares. Obviously a Foreigner could not be a citizen, but was above the slaves in that they were free members of society and not relegated to working for a master.)