The first altar mentioned in the Word was the one built by Noah after he came out of the ark, after being saved from the great flood. On that altar, he sacrificed clean animals to the Lord.

Mountains represent the Lord because of their height; we need to raise our thoughts above worldly things when "talking" with the Lord. An altar is a small artificial mountain. When it's used in worship, it can call to mind this raising of thought. The fire and smoke that rise from an altar are symbolically being sent to the Lord.

Most altars were made from unhewn stones. Stones represent truths. Unhewn stones - ones that have not been shaped by men - represent truths from the Word, truths that have not been adulterated.

The clean beasts to be sacrificed represent good things, charitable acts done because they are right. The clean birds represent thoughts about doctrine and actions, and about what is right. Presenting these things is an acknowledgment that we have them from the Lord, and a giving thanks to Him for them.

In the Israelitish Tabernacle, the altar of burnt offering represented the acknowledgment of good and the altar of incense that of truth. For this reason this larger altar, which was outside by the door, was made of brass which signifies natural good, while the altar of incense was made of gold, which signifies love to the Lord from whom comes truth.

395. 'Anyone killing Cain, vengeance will be taken on him sevenfold' means that to violate faith thus separated was utterly forbidden. This is clear from the meaning of 'Cain' as separated faith, and from the meaning of 'seven' as utterly inviolable. As is well known, the number seven was considered holy on account of the six days of creation and of the seventh, which is the celestial man in whom peace, rest, and the Sabbath exist. This is the reason why the number seven occurs so many times in the religious ceremonies of the Jewish Church, in every instance standing for that which is holy. It is also the reason why periods of time, long as well as short, were divided into seven, and were called weeks, as in the case of the long time intervals leading up to the time when the Messiah was to come, Daniel 9:24-25. A period of seven years is also called a week by Laban and Jacob, Genesis 29:27-28. Consequently wherever the number seven occurs it stands either for something holy or else for something utterly inviolable, as in David,

Seven times in the day I praise You. Psalms 119:164.

In Isaiah,

The light of the moon will be as the light of the sun, and the light of the sun will be sevenfold, as the light of seven days. Isaiah 30:26.

Here 'the sun' is love, and 'the moon' faith deriving from love, a faith which is to be as love.

[2] Just as the periods of man's regeneration divide into six before he reaches the seventh, which is the celestial man, so also do the periods of vastation even until nothing celestial is left. This was represented by the many captivities of the Jews, and by the last of them, the Babylonian, which was a captivity of seven decades, that is, seventy years. And it was several times stated that the land had to rest during its Sabbaths. It was also represented by Nebuchadnezzar, of whom it is said in Daniel,

His heart will be changed from man, and the heart of a beast given him until seven times will pass over him. Daniel 4:16, 25, 32.

In reference to the vastation of the last times it is recorded in John,

I saw another sign in heaven, great and wonderful - seven angels holding the seven Revelation 15:1, 6-7.

They will trample over the holy city for forty-two months (that is, six times seven). Revelation 11:2.

In the same book,

I saw a book [written] within and on the back, sealed with seven seals. Revelation 5:1.

Severe and increased penalties were for the same reason expressed by the number seven, as in Moses,

If you will not obey Me in this matter, I will chastise you seven times worse for your sins. Leviticus 26:18, 21, 24, 28.

In David,

Return to our neighbours sevenfold into their bosom. Psalms 79:12.

So then, it is because it was utterly forbidden to violate faith - since it had a use to serve, as has been stated - that the statement is made about 'vengeance being taken sevenfold on him who killed Cain'.