In The Name of Allaah, The Most Merciful, The Bestower of Mercy.

One of those places [in the Qur’aan] where the Prophet [sallal  laahu alayhi wasallam] was commanded to supplicate to Allaah as follows: [وَقُل رَّبِّ زِدۡنِى عِلۡمً۬ا  – And say: “My Lord! Increase me in knowledge]. [Surah Tahaa. Aayah 114]

Imaam At-Tabariy [rahimahullaah] said that this means, “Say O Muhammad! My Lord, increase me in knowledge in addition to what You have taught me”. So Allaah commanded the Messenger [sallal laahu alayhi wasallam] to ask Him for those benefits of knowledge which he does not know.

Imaam As-Sadi [rahimahullaah] said: Allaah command the Prophet [sallal laahu alayhi wasallam] to ask for an increase in knowledge, for indeed knowledge is something good and abundant good is something to be sought after; it is bestowed by Allaah and the path leading to it are: earnest striving, desiring for knowledge, asking Allaah, seeking Allaah’s Aid and Assistance, and declaring one’s need and poverty in Allaah’s presence in every instance. Indeed, the fact that the Prophet [sallal laahu alayhi wasallam] gave importance to this supplication is something well established in the [authentic] Sunnah. In a hadeeth reported by Tirmidhee and Ibn Maajah, Abu Hurairah [radiyallaahu  anhu] said: The Messenger [sallal laahu alayhi wasallam] used to say: [للَّهُمَّ انْفَعْنِي بِمَا عَلَّمْتَنِي، وَعَلِّمْنِي مَا يَنْفَعُنِي، وَزِدْنِي عِلْمًا – O Allaah! Benefit me through that which You have taught me; teach me what benefits me and increase me in knowledge].

Sufyaan Bin Uyaynah [rahimahullaah] said, “The Prophet [sallal laahu alayhi wasallam] did not cease in increasing in knowledge till the time death”.

Also the Salafus Saaleh [pious predecessors] constantly gave importance to this supplication due to that which Sa’eed Bin Mansoor and Abd Bin Humaid [rahimahumallaah] reported that Ibn Mas’ood [radiyallaahu anhu] used to supplicate, saying:

اللهم زِدْنِي إيمَانًا وَفِقْهًا وَيَقِينًا وَعِلْمًا

O Allaah! Increase me in Eemaan, understanding, certainty and knowledge.

And it has been reported from Imaam Maalik Bin Ana’s [rahimahullaah] that he said, “The situation of the son of Aadam is that he does not know everything; the situation of the son of Aadam is that he knows and then forgets; the situation of the son of Aadam is that he should ask Allaah for knowledge to add to the knowledge he already has”.

[An Excerpt from ‘Fiqh Al-Adiyah Wal Adkaar Vol 4. Page 426-427 by Shaikh Abdur Razzaaq Al-Badr [hafidhahullaah]. Slightly paraphrased]