A short and certainly not an exhaustive list of Inventions and Technological Advancements during the medieval era (roughly 500 AD to 1500 AD, though the ‘Renaissance’ itself a Christian-medieval phenomenon, instigated by Byzantium’s decline and the Turkish Jihad, is sometimes and incorrectly considered a separate era from 1400-1550.

Inventions and Technological Advancements (Chronological Order)

Algebra (3rd Century): A powerful mathematical system using symbols to represent numbers and operations was developed (Dionysius, Greeks and Christians in Alexandria, has nothing to do with Muslims)

Bookbinding with Vellum (5th Century): Animal skins were treated to create a durable and smooth writing surface for books and manuscripts.

Astrolabe (Byzantine) (5th Century): This intricate instrument was used by sailors and astronomers to determine latitude and time.

Church Schools (7th Century): Formal institutions of learning were established by the Church to educate clergy and preserve knowledge.

Horse Collar (8th Century): This improved harness allowed horses to pull heavier loads more efficiently, revolutionizing agriculture and transportation.

Stirrup (8th Century): This simple invention provided riders with greater stability and control on horseback, transforming warfare and travel.

Mounted Knight (8th Century): Combining the stirrup and horse collar, the heavily armored mounted knight became a dominant force on the battlefield.

Watermills (Early Medieval): Harnessing the power of water, these mills were used to grind grain, power machinery, and perform other tasks.

3-Field Rotation Farming (Early Medieval, widespread by 9th century): This agricultural technique increased crop yields and improved soil fertility by rotating crops across three fields.

Improved Livestock Breeding (Throughout the period, with significant advancements by the High Middle Ages): Selective breeding practices led to larger, healthier, and more productive livestock.

Clearing of Marshes and Woodlands (Throughout the period, with regional variations): Land was cleared for agriculture and settlement, expanding the areas suitable for human use.

University (12th Century): Centers of higher learning emerged, offering formal education in a variety of subjects and fostering intellectual exchange.

Windmills (12th Century): These structures harnessed wind power to grind grain, pump water, and perform other tasks, particularly in areas with limited water resources.

Flying Buttresses (12th Century, Gothic architecture): These external supports allowed for taller, thinner walls and larger windows in Gothic cathedrals.

Pointed Arches (12th Century, Gothic architecture): This architectural element distributed weight more effectively, allowing for higher ceilings and more open spaces in Gothic buildings.

Stained Glass (Primarily 12th-13th Century, Gothic period): Vibrant colored glass windows were used to illuminate and decorate Gothic cathedrals, depicting religious scenes and stories.

Physics (at Chartres) (13th Century): The study of motion, forces, and energy advanced at the Cathedral School of Chartres, laying the groundwork for later scientific breakthroughs.

Euclid's Elements (translations) (13th Century): This foundational text on geometry was translated into Latin, making its knowledge accessible to European scholars.

Reclaiming the Sea using Windmills (Holland) (13th Century onwards): Windmills were used to pump water and drain land in the Netherlands, creating new agricultural areas and settlements.

Eyeglasses (13th Century): This invention improved vision and quality of life for many, particularly those with age-related vision decline.

Mechanical clocks (14th Century onwards): Priest Richard of Wallingford in St. Albans built the first mechanical clock in the world.

Shipbuilding Improvements (Throughout the period, with advancements in various centuries): Innovations in ship design and construction led to larger, more seaworthy vessels, enabling longer voyages and increased trade.

Sails and Rigging Improvements (Throughout the period, with advancements in various centuries): More efficient sails and rigging systems improved ship maneuverability and speed.

Blast Furnaces (14th/15th Century): These furnaces produced higher temperatures, enabling the production of stronger and more versatile iron.

Printing Press (1440): Johannes Gutenberg's invention revolutionized communication and knowledge dissemination by enabling the mass production of books.

Astronomical Observatories (16th Century): Dedicated facilities for astronomical observation were established, leading to more accurate measurements and a better understanding of the universe.

Improved Steel (Throughout the period, with advancements in various centuries): Techniques for producing stronger and more durable steel were developed, improving tools, weapons, and construction materials. 

Improvements in Medicine (Throughout the period, with advancements in various centuries, eg. The use of willow bark was a development that was used throughout the entire period): Medical knowledge and practices advanced, including the use of herbal remedies, surgical techniques, and the study of anatomy.

We can also add the Jesuits and their great contributions to maths and science.