The third aliyah begins with the words "when you build a new house", and the previous aliyah ended with the mitzvah of sending away the mother bird. Rashi says that the fact that these verses are adjoined in the Torah means an additional reward for sending away the mother bird, and that is that you will build a new house. This aliyah goes on to specify the mitzvah of building a fence around a flat roof so that no one will fall off.
The aliyah then goes on to discuss some prohibited combinations. It mentions the prohibition of mixing seeds in planting, or of different species of animals plowing together. Here also is the prohibition of shatnez, which is wearing a garment containing both wool and linen, which is why we bring certain new garments to a "shatnez" checker before wearing it.
Finally the aliyah discusses some prohibited relationships between people and the prohibition of a mamzer (which is a child born from an adulterous relationship) from marrying a Jew. This underscores the urgency of a couple who is divorced only in a civil manner, to also get a kosher Jewish divorce (a "get") because without one, a subsequent relationship could be considered an adulterous relationship, causing any offspring to be mamzerim.