One should feel fortunate to start his journey of memorizing Quran. It is the message of our creator (Al-Khaliq). What else can be more important than this in this temporary life. The reward of memorizing Quran is enormous. There are many hadith regarding this, only few are mentioned below:

[Al Bukhari] “The likeness of the one who reads Quran and memorizes it, is that he is with the righteous honorable scribes. The likeness of the one who reads it and tries hard to memorize it even though it is difficult for him, he will have two rewards.” 

(Sahih Bukhari 4/1882, No. 4653.) 

[Al Bukhari] “The best amongst you is the one who learns the Quran and teaches it.” (Al-Bukhari IF 4661 IN 5027)

[Al Bukhari] “The one who recites the Quran and learns it by heart, will be with the noble righteous scribes (in Heaven) and the one who exerts himself to learn the Quran by heart and recites it with great difficulty, will have a double reward.” (Sahih Bukhari 6/2743, Sahih Muslim 1/549)

[Al Muslim] It was narrated from ‘Aamir ibn Waathilah that Naafi’ ibn ‘Abd al-Haarith met ‘Umar in ‘Usfaan, and ‘Umar had appointed him as governor of Makkah. ‘Umar said, “Who have you appointed in charge of the people of the valley?” He said, “Ibn Abza.” ‘Umar asked, “Who is Ibn Abza?” He said, “One of our freed slaves.” Umar said, “Have you appointed over them a freed slave?!” He said, “He is well-versed in the Book of Allah and he has knowledge of the laws of inheritance.” ‘Umar said: “Your Prophet (peace and blessings of Allah be upon him) said: ‘Indeed, by this Book, Allah would exalt some people and degrade others.’” (Takhreez Qutubut Sittah: Muslim 817, Ahmad 233, Darimi 3365. Tahqiq al-Albani: Sahih. Takhreez Albani: Sahih 2239.)

 [Abu Dawud] “It will be said to the companion of the Quran after he has entered Paradise, ‘Recite, and rise!’ For every verse he recites he will rise one level (in Paradise), until he recites the last verse with him (i.e., in his memory).”  (Sunan Tirmidhi, No. 2915, Abu Dawud 2/73, Sahih Ibn Hibban 3/43, Mawariduz Jaman 6/16, Majmauz Ghawaid 7/162)

[Al Thirmidhi] “Anyone who knows the Quran by heart and follows the lawful and the prohibited according to it, he will be sent to Heaven by Allah.”  (Zaif Tirmidhi Ha/2905; “Fazaelul Qur’an” chapter; Mishkat Ha/2141) 

[Al-Tirmidhi] “It will be said to the companion of the Quran: Recite and rise in status, recite as you used to recite in the world, for your status will be at the last verse that you recite.” (Sunan Tirmidhi, No. 2915, Abu Dawud 2/73, Sahih Ibn Hibban 3/43, Mawariduz Jaman 6/16, Majmauz Ghawaid 7/162)

There are many more hadiths regarding the benefits of studying Quran. May Allah give us the understanding of how important hifz Quran is. May Allah guide our soul to deen. O Allah, the Turner of the hearts, turn our hearts to your obedience. Ameen.