Any case where there is a marriage

and no violation

the [status of the] offspring follows the father;

and what is that?

A Kohenes, Leviah or Yisroelis

that marry a Kohen, Levi or Yisroel.

And any case where there is a marriage

and a violation

the offspring follows the defect;

and what is that?

A widow to a Kohen Gadol,

or a divorcee or chalutzah to a regular Kohen,

a mamzeres or Nesinah to a Yisroel

and a daughter of a Yisroel to a mamzer or Nesin.

And any woman who cannot be married to him

but can marry others

the offspring is a mamzer;

and what is that?

One who has relations with any of the relatives listed in the Torah.

And any woman who cannot have,

neither with him or with any other men, marriage

the offspring is like her;

and what is that?

The offspring of a [non-Jewish] maidservant or gentile.

Rabbi Tarfon says

Mamzerim are able to purify [their offsrping].

How?

A mamzer that marries a [non-Jewish] maidservant,

the offspring is a slave,

he is freed

and the son becomes a free man.

Rabbi Eliezer says

[the offsring is both] a slave and a mamzer.