In last week's parsha, Shmos, the Jewish people became enslaved in Egypt with hard bondage and Moshe Rabeinu was appointed by G-d to say "Let my people go" to Pharaoh. When Moshe first announced the redemption to the Jews and to Pharaoh, conditions initially became worse, i.e. they were in an even darker golus (exile).
The first aliyah continues the conversation between Moshe and G-d after the Jews were denied the straw and Moshe said to G-d: "Why did You deal ill with Your people?" G-d responds by reviewing the history of His relationship with the patriarchs.
G-d says the patriarchs didn't know G-d's name of Havayah. (The previous use of the name "Elokim" was G-d's name in the language of gevurah [judgment] and limitation -- e.g. creation of a world that looks natural happens with the name "Elokim". The Divine name of Havayah is the language of chesed [kindness] and limitless. As we read last week, the Jewish women were giving birth to seemingly limitless children and the population was increasing in an unlimited way and the world was about to see wonders and miracles as they had never seen before.)
G-d reviews His covenant that He made with each of the patriarchs to give them the land of Canaan. G-d adds that He is aware of the Jewish people's suffering.
Moshe then tells all this to the people, but they are upset with their increased burden and don't listen.
G-d says "Go tell Pharaoh that he should send away the Jews". Moshe responds: "The Jews don't listen to me, how is Pharaoh going to hear me?" G-d adds Aharon, Moshe's brother, with Moshe as a spokesman and a mediator and gave them a charge to bring the Jews out of Egypt.
In the second aliyah the Torah traces the lineage of Moshe and Aharon by listing their family trees, and then returns to the subject of their current conversation with G-d.
In the third aliyah, the Torah resumes the conversation of G-d and Moshe by repeating elements of it such as Moshe should go speak to Pharaoh, and Moshe answering that he is of "uncircumcised" lips - meaning he felt limited in being able to speak.
G-d says "I am G-d" -- Rashi says that G-d is saying here to Moshe that G-d is competent to send Moshe. Or as it has been said: "When you are doing what G-d wants, you have infinite power".
Moshe is told to go speak to Pharaoh, with Aharon as spokesman, telling Pharaoh that he should let G-d's people go. He is further told that G-d will harden Pharaoh's heart in order to multiply G-d's wonders in Egypt such that Egyptians should know that G-d is the L-rd.
Moshe and Aharon do as G-d tells them, and the aliyah ends by stating that Moshe is 80 years old and Aharon is 83 when they speak to Pharaoh.
In the fourth aliyah Moshe tries to impress upon Pharaoh Who sent him by Moshe casting down his rod in front of Pharaoh and it turning into a serpent. But Pharaoh isn't impressed.
Next are the first two plagues of Egypt: blood and frogs. Moshe meets Pharaoh early in the morning by the Nile River. (Pharaoh maintained that he was a god and didn't need a bathroom but Pharaoh would sneak off to the river early in the morning to use the bathroom.) Moshe tells Aharon to smite the river. The river and all the water in Egypt (including in vessels) turns to blood and all the fish die. Moshe specifically does this through Aharon because Moshe was protected by the river when he was a baby (says Rashi). The plague of blood lasts seven days.
Next, the plague of frogs begins, where frogs come out of the river and cover the land, enter all the houses, and their ovens and their bowls. Rashi says that the frogs even entered the internal organs of the people and the frogs croaked there.
The Lubavitcher Rebbe explained that a lesson we can derive from the frogs action is that even though the frog hates heat - that's why they are always in or near water - nevertheless, since they were on a mission for G-d they did things against their inherent nature.
At the end of the previous aliyah Pharaoh says he will let the people go if the frogs go away. So in this, the fifth aliyah, Moshe asks G-d to make the frogs go away on the day Pharaoh asks, so as to impress Pharaoh with the power of G-d. The frogs die and Egypt smells very bad from their odor. But Pharaoh backs out, and doesn't let the Jews go. Then two more plagues happen in this aliyah:
G-d tells Moshe to tell Aharon to smite the dust of the earth so that it becomes lice (Moshe couldn't smite the dust himself since the dust had hid the Egyptian Moshe killed - Rashi). The plague of lice begins, with lice covering man and beast -- Even the magicians of Egypt were impressed and they told Pharaoh that this is the "finger of G-d".
Pharaoh doesn't change his mind, so G-d tells Moshe to warn Pharaoh about the next plague, which will be the plague of noxious animals. Serpents and scorpions will cover Egypt and fill their houses, but they will leave alone the land of Goshen, where the Jews live.
In the sixth aliyah G-d starts the plague of noxious animals with serpents and scorpions swarming into Pharaoh's palace and everyone else's house in Egypt, and the land is ruined except for the land of Goshen. Pharaoh calls Moshe and Aharon and tells them that the Jews can sacrifice to G-d. The plague ends and Pharaoh changes his mind and reneges on his promise.
Next is the plague of heavy pestilence on the Egyptians' cattle, horses, donkeys, camels, herds and flocks. All of these animals die, but none of the Jews' animals are affected.
Next is the plague of extremely painful leprous boils that cover all Egyptian men and beasts; but Pharaoh still doesn't release the Jews.
In the seventh aliyah G-d warns that every man or beast found in the field will be smitten with a most grievous hail. Those that fear G-d bring themselves and their cattle in from the field. Moshe stretches his rod toward heaven and a fiery hail comes down to earth such as never had been seen before. Everything that is in the field, both man, beast, and every herb and tree is destroyed except in the land of Goshen where there is no hail.
Pharaoh now admits his sin and says that he recognizes the righteousness of G-d. The plague stops, but Pharaoh changes his mind again.