What are the Qur'anic surahs and verses, and prophetic hadiths that every Muslim should memorize, learn, and act upon?

Religious knowledge is divided into Fardh Ain (individual obligation) and Fardh Kifayah (communal obligation). Fardh Ain is that knowledge upon which the understanding of acts of worship and transactions depends. Fardh Kifayah is that which, if undertaken by some, absolves others. Memorizing the Quran and Hadith are among the Furoodh Kifayah (plural of Fardh Kifayah), while it is not individually obligatory to memorize any part of them, except for what is indispensable for the validity of prayer, such as Al-Fatiha, which must be learned and recited proficiently, even if from a Mushaf (copy of the Quran), as well as learning the words of the Tashahhud. Therefore, if someone does not learn Al-Fatiha despite being able to, their prayer is invalid.