Active Record is an essential component of the Ruby on Rails framework, acting as an Object-Relational Mapping (ORM) layer that facilitates database interactions by abstracting complexities. With Active Record, developers can seamlessly manipulate database records using Ruby objects, turning database tables into easily manageable classes. This means that instead of writing verbose SQL queries, developers can interact with their data using straightforward and intuitive Ruby methods, thereby improving productivity and reducing the likelihood of errors.

One of the key features of Active Record is its ability to define relationships between different models. These relationships can be one-to-many, many-to-many, or one-to-one, and they allow developers to efficiently retrieve associated data with minimal effort. For instance, using the has_many and belongs_to associations, developers can easily load related records, making data manipulation cleaner and more coherent. By understanding and utilizing Active Record, developers can significantly enhance the scalability and maintainability of their Ruby on Rails applications.

When developing applications with Ruby on Rails, it's crucial to avoid common mistakes that can lead to performance issues and hinder scalability. One major mistake is skipping automated tests. While Rails encourages testing, many developers underestimate its importance and only test critical features. This oversight often results in bugs that appear later in the development lifecycle. To mitigate this, always implement a comprehensive testing strategy that includes unit, integration, and system tests, ensuring that every aspect of your application functions as expected.

Another frequent error is neglecting database optimizations, such as failing to use indexes effectively. Rails provides conventions for database structure, but without the proper use of indexes, even simple queries can slow down your application's performance significantly. Remember to analyze your database queries and utilize tools like Active Record to identify and implement necessary indexes, thereby enhancing the overall efficiency of your application.

Building a RESTful API with Ruby on Rails is a straightforward process that can enhance the scalability and maintainability of your application. To begin, ensure you have Ruby on Rails installed on your development machine. Start a new Rails project by running rails new my_api --api, which creates a lightweight application optimized for API-only purposes. After that, define your resources within the config/routes.rb file using the resources method to map HTTP verbs to controller actions.

Next, create a controller that will handle your API's requests. Generate a new controller with rails generate controller Api::V1::Items, and define your actions like index, show, create, update, and destroy to manage the different requests. Don’t forget to structure your responses in JSON format for better compatibility with clients. Implementing authentication and authorization is also crucial to secure your API while using tools like Devise or JWT for user management. Follow these steps, and you'll have a fully functional RESTful API in no time!