Every week, the Jews read a portion from the Torah. Each portion is called a parashah or parashat. The whole Torah is read through in one Jewish year. They also read from the Haftarah which is a reading from the prophets. Messianic Jews also add a reading from the Apostolic Writings or B’rit Hadashah/New Covenant.
Although the Jews are agreed as to the Torah portion, there are some differences as to what is read by some groups for the Haftarah. There is no particular schedule of B’rit Hadashah readings.
For more information on Torah and the Torah Reading Cycle go here.
First Fruits of Zion (FFOZ) has a wonderful Torah Club with teachings from the scriptures every week. They have taken portions from the Torah Club Volumes and put them online for free. You need to sign up to see them, but there is no cost. To see them, go here.
Hebrew4Christians also has some good information. Parashat Summaries
Sondra Baras teaches on CFOIC. Shabbat Shalom
You can also find teaching about the Parashot at Root Source. They are mixed in to their blog posts. Root Source Blog (Root Source also has some wonderful teachings on a variety of subjects. Check them out!)