Rule 1: 1. The superlative أَعْلَى and its feminine اَلْعُلْيَا
You know the elative pattern أَفْعَلُ from lesson 52: أَكْبَرُ, أَطْوَلُ. When the third radical is و or ي the pattern ends in alif maqṣūra: عَالٍ high (root ع ل و) gives أَعْلَى higher, highest; دَانٍ near, low gives أَدْنَى. The elative has a special feminine on the pattern فُعْلَى, used when the superlative is definite and describes a feminine noun: اَلْعُلْيَا, اَلدُّنْيَا, اَلْكُبْرَى, اَلصُّغْرَى, اَلْأُولَى (from أَوَّلُ). With مِنْ than, the masculine أَفْعَلُ serves for both genders and never changes.
نَظَرَتِ الْمَحْكَمَةُ الْعُلْيَا فِي الْقَضِيَّةِ.
naẓarati l-maḥkamatu l-ʿulyā fi l-qaḍiyyati
The supreme court examined the case.
Feminine noun, definite superlative: فُعْلَى.
اِجْتَمَعَ الْمَجْلِسُ الْأَعْلَى لِلتَّعْلِيمِ أَمْسِ.
ijtamaʿa l-majlisu l-aʿlā li-t-taʿlīmi amsi
The supreme council for education met yesterday.
Masculine noun: أَفْعَلُ with the article.
هٰذِهِ الْمَحْكَمَةُ أَعْلَى مِنْ تِلْكَ.
hādhihi l-maḥkamatu aʿlā min tilka
This court is higher than that one.
With مِنْ the form is invariable: not عُلْيَا.
اَلْجَامِعَةُ الْكُبْرَى فِي الْمَدِينَةِ قَرِيبَةٌ مِنَ الْمِينَاءِ.
al-jāmiʿatu l-kubrā fi l-madīnati qarībatun mina l-mīnāʾi
The biggest university in the city is near the port.
هٰذِهِ هِيَ الْمَرْحَلَةُ الْأُولَى مِنَ الْمَشْرُوعِ.
hādhihi hiya l-marḥalatu l-ūlā mina l-mashrūʿi
This is the first stage of the project.
اَلْأُولَى is the feminine of أَوَّلُ.
اَلْحَيَاةُ الدُّنْيَا قَصِيرَةٌ.
al-ḥayātu d-dunyā qaṣīratun
The life of this world is short.
اَلدُّنْيَا 'the nearer (life)', feminine of أَدْنَى; و after ḍamma becomes ي: دُنْوَى → دُنْيَا.