Hello! I will start with Mughal architecture:
1) The Mughals built mostly mausoleums, mosques, palaces, and forts. The Mughals were influenced by Hindu/Muslim and Persian styles. This is known as Indo-Islamic architecture.
2) Mughal architecture featured domes, minarets with cupolas, grandly constructed gateways, and ornamental design.
3) White marble was greatly favored as building material, followed by red sandstone.
4) The charbagh or garden is divided into four parts.
5) There is an extensive use of tile work.
1) The main inspiration for Renaissance architecture was Greek and Roman architecture. Liberal use of Doric, Ionic, and Corinthian orders highlighted the principles of Humanism.
2) Renaissance architecture featured mainly churches, chapels, cathedrals, palazzos (urban mansions), and villas (country mansions).
3) Buildings featured the harmony and mathematical proportion inherent in planar classicism (flat classicism). Walls were embellished with classical motifs (columns, arches, etc.).
4) Brunelleschi's octagonal dome of the Florence Cathedral featured a "true masterpiece of structural engineering, carefully designed to spread the load without creating stress."
5) The facades of buildings were often divided into rectangular sections, and each section featured an arched window. Circular elements above windows were greatly favored, as the circle was considered a perfect shape.
Further descriptions and images will be useful.
I hope the above is helpful to you. Thanks for the question!
The Mughal Empire had their own Renaissance in India. It was very similar to the European Renaissance. The Mughal's greatest advancements were in architecture. Akbar was responsible for one of the first major building projects; he constructed a huge fort at Agra and created the new capital city at Fatehpur Sikri. Jahangir was not much of a visionary, but his wife helped and had built the Mausoleum of Akbar located at Sikandra. It was a sandstone and marble masterpiece. Jahangir also helped configure the Mughal gardens; the most famous is the Shalimar Bagh on the banks of Lake Dal in Kashmir.
Emperor Shah Jahan contributed the most to Mughal architecture. He strictly used marble and not sandstone. He tore down the Red Fort built by Akbar and replaced it with marble buildings such as the Diwan-I-Am and Diwan-i-Khas. He is most famous for constructing the Taj Mahal, which he built as a memorial for his wife.
The greatest influence this had on Europe was the use of marble. India helped bring the beauty of marble to Europe, which added an interesting contrast to European architecture in the form of large colorful gardens, textured surfaces and patterns, and the Mughal's inspired naturalism in which animals were depicted realistically and accurately.