What are the essential books a student of knowledge should have in their library across various disciplines?

It is possible to mention some useful Islamic books in various disciplines:

In the Quran and its sciences: The Holy Quran, Tafsir Ibn Kathir, Ulum al-Quran by Manna al-Qattan, Ahkam al-Quran by Ibn al-Arabi, Haqq al-Tilawah, and Al-Nashr fi al-Qira'at al-Ashr.

In Aqeedah (creed) and Tawhid (monotheism): Kitab al-Tawhid and its commentaries, Al-Aqeedah al-Wasitiyyah and its commentaries, Al-Aqeedah al-Tahawiyyah and its commentaries, Ma'arij al-Qabul, and Lum'at al-I'tiqad by Ibn Qudamah.

In Seerah (Prophet's biography): Al-Raheeq Al-Makhtum, Fiqh al-Seerah, and Seerat Ibn Hisham.

In Fiqh (jurisprudence) (e.g., for the Shafi'i school): Matn Abi Shuja' and its commentaries, Matn al-Minhaj and its commentaries, and Manzumat al-Zubad and its commentaries.

In Hadith: Al-Arba'in al-Nawawiyyah and its commentaries, Jami' al-Ulum wal-Hikam, Umdat al-Ahkam, Riyad al-Salihin, Al-Lu'lu' wal-Marjan, Nayl al-Awtar, and the books of Sunnah such as the Two Sahihs and the Four Sunans.

In Usul al-Fiqh (principles of jurisprudence): Matn al-Waraqat, Maraqi al-Sa'ud, Rawdat al-Nazir, Jam' al-Jawami', and Usul al-Fiqh by Abd al-Wahhab Khallaf.

In Usul al-Hadith (principles of Hadith): Al-Taqrib by Al-Nawawi and its commentary by Al-Suyuti, Muqaddimat Ibn al-Salah, Ikhtisar Ibn Kathir and its commentary by Ahmad Shakir, Nuzhat al-Nazar, and Alfiyyat al-Iraqi and its commentaries.

In Arabic Language: Al-Ajurrumiyyah and its commentary, Mutammimat al-Ajurrumiyyah, Qatr al-Nada, Alfiyyat Ibn Malik and its commentary, Shadhaa al-Arf fi Fan al-Sarf, Al-Balaghah al-Wadihah, and Jawahir al-Adab.

In Raqa'iq (heart-softeners): Al-Bahr al-Ra'iq, Madarij al-Salikin or its abridgment, and Mukhtasar Minhaj al-Qasidin.

In Fiqh قواعد (jurisprudential maxims) and Maqasid al-Sharia (objectives of Islamic law): Manzumat Ibn Sa'di and its commentary, Manzumat al-Ahdal and its commentaries, Al-Qawa'id al-Fiqhiyyah by Al-Nawawi, Al-Wajeez by Al-Burnu, Al-Muwafaqat by Al-Shatibi, Qawa'id al-Ahkam by Ibn Abd al-Salam, Al-Furuq by Al-Iraqi, and Al-Ashbah wal-Naza'ir by Al-Suyuti.

In Fatawa (religious edicts): Fatawa Ibn Taymiyyah, Fatawa al-Lajnah al-Da'imah (Permanent Committee), and decisions of the Fiqh Council.

In Administration and Planning: Hatta La Takuna Kalla (So That You Are Not Nothing), The Seven Habits of Highly Effective People, and Problem Solving.

If the questioner cannot afford to buy all of them, let him buy what is available and start with the abridgments.