Before memorising any rules, it helps to understand what tajwid actually is, why it exists, and where it sits in the practice of reciting the Qur'an.
Linguistically, tajwid ( تَجْوِيد ) comes from jawwada, meaning to make something good or to perfect it. Technically, tajwid is the knowledge of reciting the Qur'an by giving every letter its correct articulation point (makhraj) along with its due rights (haqq) and its required characteristics (mustahaqq) — the qualities inherent to it and the rules that arise when letters meet.
The primary basis for reciting with tartil is the words of Allah: وَرَتِّلِ الْقُرْآنَ تَرْتِيلًا — “and recite the Qur'an with measured recitation.” (Surah Al-Muzzammil 73:4). Tajwid is how that tartil is put into practice.
According to the majority (jumhur) of scholars there are two sides to this. Studying the theory of tajwid is fardhu kifayah — a communal obligation, sufficiently fulfilled if some members of a community take it on. Reciting the Qur'an in accordance with tajwid — at minimum avoiding clear errors (lahn jali) — is considered fardhu 'ain, an individual obligation on each Muslim who recites. In other words: not everyone must become a theorist, but each person is expected to recite as well as they are able and to keep improving.
If you're just starting, continue with How to Learn Tajwid from Scratch and The Right Order to Learn Tajwid, or browse the complete list of tajwid rules with examples and audio.
According to the majority of scholars, studying the theory of tajwid is fardhu kifayah (a communal obligation), while reciting the Qur'an according to tajwid — at minimum avoiding clear errors (lahn jali) — is fardhu 'ain for every Muslim who recites.
The verse most often cited is Surah Al-Muzzammil 73:4: 'wa rattilil-qur'āna tartīlā' — and recite the Qur'an with measured recitation. Tajwid is how that measured recitation is realised in practice.
Linguistically tajwid means to make good or to perfect, from the root jawwada. Technically it is the knowledge of reciting the Qur'an by giving each letter its proper articulation point together with its due rights (haqq) and required characteristics (mustahaqq).