In last week's parsha, parsha Bo, the Jews were miraculously redeemed from their slavery in Egypt after ten wondrous plagues of Egypt culminating with the plague of the death of the first born of Egypt. This parsha continues the story as the Jewish nation continues their escape.
In the first aliyah, G-d initially leads the Jews in a round about way for two reasons: first was to avoid an immediate war with the Philistine nation (which was on a more direct route) which might cause the Jews to regret leaving Egypt. Second, to appear to be lost to the Egyptians, so they will be encouraged to pursue after them.
Moshe takes the bones of Yosef with him as Yosef had made them promise to do when their redemption came. They were led by G-d, by day in a pillar of cloud, and by night by a pillar of fire.
Pharaoh and the Egyptians regretted letting them leave (Rashi says: because of the money the Jews took that their Egyptian neighbors freely gave them as they left) and pursued after them 600 chariots strong.
In the second aliyah, the pursuing Egyptians corner the Jews by the Yam Suf (Sea of Reeds), and the Jews realize their predicament and ask Moshe if he brought them out of Egypt only to die in the wilderness.
Moshe answers them that now they will see the salvation of G-d; now they see the Egyptians, soon after they will never see them again.
In the third aliyah G-d says to Moshe: stretch out your hand over the sea and divide it, and the Jews will go forward in the midst of the sea over dry land.
Moshe stretches out his hands and the sea divides. (Actually, the sea divides into twelve paths -- one for each tribe. We are told that when Moshiach comes, may it be speedily in our days, the sea will similarly divide, but into only seven paths). Rashi says that the waters of the whole world divided along with the Yam Suf.
G-d removes Himself from leading the way before the Jews to following after them. This is in order to go between the Jews and the Egyptians to protect the Jews by absorbing the Egyptian's arrows and catapulted stones (says Rashi).
The pillar of cloud also goes behind the Jews to cause darkness for the Egyptians.
The waters are a wall on each side of the Jews and they walk on dry land in the midst of the sea.
The Egyptians pursue after them, including all of Pharaoh's horses and chariots.
G-d takes off the wheels from the Egyptian's chariots, and the Egyptians say, "Let us flee from Israel, because G-d fights for them".
In the fourth aliyah, at G-d's direction, Moshe stretches his hand over the sea and the waters return and cover the Egyptians.
The Egyptians wash up dead on the seashore. (Rashi says: to prove that they didn't escape to the other side only to attack again at a later date and be a source of further anxiety).
Then Moshe and the Jews sing the song "Az Yashir" praising G-d (this is also part of our daily Morning Prayer, on page 39 of the Siddur Tehillat Hashem).
Following this, Miriam, Moshe's sister, with the women, sing with their tambourines (which they had brought from Egypt specifically because they knew that G-d would do great miracles for them). (Many women today keep tambourines in their houses in preparation for the final redemption, which we expect momentarily.)
The word used here to mean "sing" -- "Yashir," is in the future tense, indicating that this song will be used again at the time of Techiyas Hameisim - (resurrection of the dead), which will happen along with Moshiach's coming, may it be speedily in our days!
G-d then gives the Jewish Nation some Chukim -- commandments without readily human understandable reasons -- and said that if the Jews keep all of G-d's Chukim, then G-d will not afflict the Jews with any of the diseases of Egypt. G-d then concludes that He is the G-d that heals them.
This alludes to the matter that just as a doctor says "don't eat this thing and it will be well with you," G-d, the one who created us, surely knows what is good for us and tells us how to live, with His Torah.
In the fifth aliyah, the Jews run out of the matzo they brought with them from Egypt. They murmur that at least in Egypt they had plenty of bread to eat, and here it appears to them that they will die of hunger.
G-d answers that He will provide quail and manna for them to eat, and that each day they should gather only what they need for one day, but on Friday they will have enough for two days (to provide for Shabbos)
In the sixth aliyah, the quails appear in the evening.
In the morning, manna appears with a layer of dew above and below it (this is why our Shabbos challah is on top of a board and covered with a challah cover).
The Jews are told to gather one omer (a biblical measure of approximately .5 liters or 5.2 pints) of it, and he who gathers more or less than an omer arrives home with exactly one omer.
They are told not to leave any over till the next day, and those that do so find it rotted with worms.
On Friday they are given two portions of manna, this is a reason why on Shabbos we make the Hamotzi blessing (for bread) over two loaves of challah. They are told to leave over the second portion for Shabbos, and not to leave their premises to look for manna on the Shabbos because there would be none found.
This is when they are given the Shabbos, as a day of rest, and they are told to cook on Friday and lay it up for Shabbos (as in cholent).
In the seventh aliyah, the Jews journey further and run out of water and complain to Moshe. Moshe relays this to G-d and G-d tells him to smite a certain rock with his staff so that water will come out of it for the people to drink.
Then the nation of Amalak comes and fights with Israel. They are always remembered as the first ones to attack the Jews, thereby breaking the ice, so to speak, showing other nations their example of making war with the Jews. Our sages tell us that the wicked Haman descended from Amalak.
Another aspect of this war of Amalak is that they attacked on the Jews' way to Mt. Sinai to receive the Torah, and therefore attempted to dampen their enthusiasm for receiving the Torah by causing trouble on the way.
Chassidus teaches that whenever our enthusiasm for a mitzvah is dampened, it's our personal internal Amalak doing it to us, and we are enjoined to blot it out. It is interesting to note that the word for "doubt" in Hebrew, is "sofek", which has the same gematria (numerical value) as Amalak (240). So whenever we have a doubt that slows or prevents a mitzvah, that is Amalak slowing or preventing that mitzvah.