A camera controller for easily flying around a scene in Unity smoothly. WASD for lateral movement, Space & Ctrl for vertical movement, Shift to move faster. Add this script to an existing camera, or an empty game object, hit play, and you're ready to go~

FlyCamera.cs

using UnityEngine;

[RequireComponent( typeof(Camera) )]
public class FlyCamera : MonoBehaviour {
	public float acceleration = 50; // how fast you accelerate
	public float accSprintMultiplier = 4; // how much faster you go when "sprinting"
	public float lookSensitivity = 1; // mouse look sensitivity
	public float dampingCoefficient = 5; // how quickly you break to a halt after you stop your input
	public bool focusOnEnable = true; // whether or not to focus and lock cursor immediately on enable

	Vector3 velocity; // current velocity

	static bool Focused {
		get => Cursor.lockState == CursorLockMode.Locked;
		set {
			Cursor.lockState = value ? CursorLockMode.Locked : CursorLockMode.None;
			Cursor.visible = value == false;
		}
	}

	void OnEnable() {
		if( focusOnEnable ) Focused = true;
	}

	void OnDisable() => Focused = false;

	void Update() {
		// Input
		if( Focused )
			UpdateInput();
		else if( Input.GetMouseButtonDown( 0 ) )
			Focused = true;

		// Physics
		velocity = Vector3.Lerp( velocity, Vector3.zero, dampingCoefficient * Time.deltaTime );
		transform.position += velocity * Time.deltaTime;
	}

	void UpdateInput() {
		// Position
		velocity += GetAccelerationVector() * Time.deltaTime;

		// Rotation
		Vector2 mouseDelta = lookSensitivity * new Vector2( Input.GetAxis( "Mouse X" ), -Input.GetAxis( "Mouse Y" ) );
		Quaternion rotation = transform.rotation;
		Quaternion horiz = Quaternion.AngleAxis( mouseDelta.x, Vector3.up );
		Quaternion vert = Quaternion.AngleAxis( mouseDelta.y, Vector3.right );
		transform.rotation = horiz * rotation * vert;

		// Leave cursor lock
		if( Input.GetKeyDown( KeyCode.Escape ) )
			Focused = false;
	}

	Vector3 GetAccelerationVector() {
		Vector3 moveInput = default;

		void AddMovement( KeyCode key, Vector3 dir ) {
			if( Input.GetKey( key ) )
				moveInput += dir;
		}

		AddMovement( KeyCode.W, Vector3.forward );
		AddMovement( KeyCode.S, Vector3.back );
		AddMovement( KeyCode.D, Vector3.right );
		AddMovement( KeyCode.A, Vector3.left );
		AddMovement( KeyCode.Space, Vector3.up );
		AddMovement( KeyCode.LeftControl, Vector3.down );
		Vector3 direction = transform.TransformVector( moveInput.normalized );

		if( Input.GetKey( KeyCode.LeftShift ) )
			return direction * ( acceleration * accSprintMultiplier ); // "sprinting"
		return direction * acceleration; // "walking"
	}
}

@VojtaStruhar You don't need to invoke InverseTransformDirection, transform.up is the vector you need.
AddMovement( KeyCode.Space, transform.up );

Nice script. Just what I needed for viewing my math visualization :)

Awesome to test scenes, works perfectly. Thank you so much!