Allah says: this will happen on the Day of Resurrection:

﴿يَوْمَ نَطْوِى السَّمَآءَ كَطَىِّ السِّجِلِّ لِلْكُتُبِ﴾

(And (remember) the Day when We shall roll up the heaven like a Sijill for books.) This is like the Ayah:

﴿وَمَا قَدَرُواْ اللَّهَ حَقَّ قَدْرِهِ وَالاٌّرْضُ جَمِيعـاً قَبْضَـتُهُ يَوْمَ الْقِيَـمَةِ وَالسَّمَـوَتُ مَطْوِيَّـتٌ بِيَمِينِهِ سُبْحَـنَهُ وَتَعَالَى عَمَّا يُشْرِكُونَ ﴾

(They made not a just estimate of Allah such as is due to Him. And on the Day of Resurrection the whole of the earth will be grasped by His Hand and the heavens will be rolled up in His Right Hand. Glorified be He, and High be He above all that they associate as partners with Him!) ﴿39:67﴾ Al-Bukhari recorded that Nafi` reported from Ibn `Umar that the Messenger of Allah said:

«إِنَّ اللهَ يَقْبِضُ يَوْمَ الْقِيَامَةِ الْأَرَضِينَ وَتَكُونُ السَّمَوَاتُ بِيَمِينِه»

(On the Day of Resurrection, Allah will seize the earth and the heavens will be in His Right Hand.) This was recorded by Al-Bukhari, may Allah have mercy on him.

﴿كَطَىِّ السِّجِلِّ لِلْكُتُبِ﴾

(like a Sijill rolled up for books.) What is meant by Sijill is book. As-Suddi said concerning this Ayah: "As-Sijill is an angel who is entrusted with the records; when a person dies, his Book (of deeds) is taken up to As-Sijill, and he rolls it up and puts it away until the Day of Resurrection.'' But the correct view as narrated from Ibn `Abbas is that As-Sijill refers to the record (of deeds). This was also reported from him by `Ali bin Abi Talhah and Al-`Awfi. This was also stated by Mujahid, Qatadah and others. This was the view favored by Ibn Jarir, because this usage is well-known in the (Arabic) language. Based on the above, the meaning is: the Day when the heaven will be rolled up like a scroll. This is like the Ayah:

﴿فَلَمَّا أَسْلَمَا وَتَلَّهُ لِلْجَبِينِ ﴾

(Then, when they had both submitted themselves (to the will of Allah), and he had laid him prostrate on his forehead.) ﴿37:103﴾ There are many more linguistic examples in this respect. Allah knows best.

﴿كَمَا بَدَأْنَآ أَوَّلَ خَلْقٍ نُّعِيدُهُ وَعْداً عَلَيْنَآ إِنَّا كُنَّا فَـعِلِينَ﴾

(As We began the first creation, We shall repeat it. (It is) a promise binding upon Us. Truly, We shall do it.) means, this will inevitably come to pass on the Day when Allah creates His creation anew. As He created them in the first place, He is surely able to re-create them. This must inevitably come to pass because it is one of the things that Allah has promised, and He does not break His promise. He is able to do that. Because He says:

﴿إِنَّا كُنَّا فَـعِلِينَ﴾

(Truly, We shall do it.) Imam Ahmad recorded that Ibn `Abbas said: "The Messenger of Allah stood among us exhorting us, and said:

«إِنَّكُمْ مَحْشُورُونَ إِلَى اللهِ عَزَّ وَجَلَّ حُفَاةً عُرَاةً غُرْلًا، كَمَا بَدَأْنَا أَوَّلَ خَلْقٍ نُعِيدُهُ وَعْدًا عَلَيْنَا، إِنَّا كُنَّا فَاعِلِين»

(You will be gathered before Allah barefoot, naked and uncircumcised. As We began the first creation, We shall repeat it. (It is) a promise binding upon Us. Truly, We shall do it.) And he mentioned the entire Hadith. It was also recorded in the Two Sahihs, and Al-Bukhari mentioned it in his Tafsir of this Ayah.

﴿وَلَقَدْ كَتَبْنَا فِى الزَّبُورِ مِن بَعْدِ الذِّكْرِ أَنَّ الاٌّرْضَ يَرِثُهَا عِبَادِىَ الصَّـلِحُونَ - إِنَّ فِى هَـذَا لَبَلَـغاً لِّقَوْمٍ عَـبِدِينَ - وَمَآ أَرْسَلْنَـكَ إِلاَّ رَحْمَةً لِّلْعَـلَمِينَ ﴾

(105. And indeed We have written in Az-Zabur after Adh-Dhikr that My righteous servants shall inherit the land.) (106. Verily, in this there is a plain Message for people who worship Allah.) (107. And We have sent you (O Muhammad ) not but as a mercy for the `Alamin.)