The Rambam begins Sefer HaMitzvot, the “Book of Commandments”, with a list of the 248 positive (“to do”) mitzvot in the Torah. For each, he provides an exact source to where that mitzvah is given in the Torah. After this list is complete, he will go into the 365 negative (“not to do”) mitzvot in the Torah. Altogether, the Torah contains 613 commandments.
Summary: The first mitzvah of Judaism is to know that there is a God. The second mitzvah is to know that God is One. The third mitzvah is to love God. The fourth mitzvah is to fear God. The fifth mitzvah is to pray to God. The sixth mitzvah is to “cleave” to God, and seek to grow ever-closer to Him. The seventh is to swear only in the name of God. The eighth is to walk in God’s ways – “just as God is compassionate, you be compassionate; just as God is merciful, you be merciful”, etc. The ninth is to sanctify God’s Name (kiddush Hashem) – to be a model citizen so that people see what a truly God-serving person is, and will be inspired to draw closer to God as well. The tenth mitzvah is to recite Shema Israel twice a day, morning and night. The eleventh mitzvah is to learn and teach Torah. The twelfth and thirteenth mitzvahs are to put on tefillin on the head and arm (each is a separate mitzvah!) The fourteenth is to wear tzitzit fringes on the corners of one’s clothes. The fifteenth is to affix a mezuzah on the doorposts. The sixteenth is the mitzvah of Hak’hel where, in ancient times, the entire nation would gather in Jerusalem every seventh year to hear a public reading of the Torah. The seventeenth mitzvah is for each Jew to write a Torah for himself. Since it is difficult to write an entire Torah, and requires much training, this mitzvah can be fulfilled by contributing a donation towards the production of a Torah scroll, or even helping to ink in a single letter. The eighteenth is for a king of Israel to write an additional Torah scroll for himself, to ensure he will abide by it when he rules. The nineteenth is to recite birkat hamazon, the “grace after meals”, to thank God for one’s food. The twentieth is to build (or rebuild, or contribute to the building of) the Temple in Jerusalem.
Insight: The 248 positive mitzvot of the Torah correspond to the 248 evarim, or parts of the human body. (Some list these 248 as all the bones and major joints of the body, while others enumerate them as the 206 bones in an adult human body, plus 42 major organs.) Meanwhile, the 365 negative commandments correspond to the 365 major gidim, or nerves, of the body. They also correspond to the 365 days of the solar year. One who keeps all 613 commandments therefore keeps their entire body spiritually healthy. For those who like gematria (Jewish numerology), the value of “Moshe Rabbeinu” (משה רבינו) is 613, since Moses is the one that brought us the 613 commandments from God!
For a summary of the first 20 mitzvot, with further explanation, see the following short video: