Xcode
Xcode is the IDE endorsed by Apple for iOS development. The latest stable version is 13.4.1. It comes with the official iOS SDK.
Since iOS 9 / XCode 7, it is now possible by default to deploy and develop apps for your device without a $99/year developer account.
For bypassing restrictions on 7 day signing windows, see AppSync Unified
For notes about using Logos and Theos with Xcode, see Xcode Logos.
App Store Download Link: https://apps.apple.com/us/app/xcode/id497799835?mt=12
The latest stable and beta versions can also be downloaded directly from: https://developer.apple.com/download/applications/
Note this page also requires signing in with your Apple ID.