Notebook interface
A notebook interface (also called a computational notebook) is a virtual notebook environment used for literate programming, a method of writing computer programs. Some notebooks are WYSIWYG environments including executable calculations embedded in formatted documents; others separate calculations and text into separate sections.

Modular notebooks may connect to a variety of computational back ends, called "kernels". Notebook interfaces are widely used for statistics, data science, machine learning, and computer algebra.

At the notebook core is the idea of literate programming tools which can be described as "tools let you arrange the parts of a program in any order and extract documentation and code from the same source file.", the notebook takes this approach to a new level extending it with some graphic functionality and a focus on interactivity.  According to Stephen Wolfram: "The idea of a notebook is to have an interactive document that freely mixes code, results, graphics, text and everything else.", and according to the Jupyter Project Documentation: "The notebook extends the console-based approach to interactive computing in a qualitatively new direction, providing a web-based application suitable for capturing the whole computation process: developing, documenting, and executing code, as well as communicating the results. The Jupyter notebook combines two components".

History 
Research on WYSIWYG mathematical systems supporting mixed text and calculations with a document metaphor begin to be published in 1987: Ron Avitzur's Milo, William Schelter's INFOR, Xerox PARC's Tioga and CaminoReal. 

The earliest commercial system using the document metaphor was MathCAD, which also came out in 1987. Wolfram Mathematica 1.0 followed soon afterwards (1988). Later came Maple 5.2 (1992) and Macsyma 2.0 (1995).

As the notebook interface increased in popularity over the next two decades, notebooks for various computational back ends ("kernels") have been introduced, including MATLAB, Python, Julia, Scala, SQL, and others.

Use 
Notebooks are traditionally used in the sciences as electronic lab notebooks to document research procedures, data, calculations, and findings. Notebooks track methodology to make it easier to reproduce results and calculations with different data sets. In education, the notebook interface provides a digital learning environment, particularly for the teaching of computational thinking. Their utility for combining text with code makes them unique in the realm of education. Digital notebooks are sometimes used for presentations as an alternative to PowerPoint and other presentation software, as they allow for the execution of code inside the notebook environment. Due to their ability to display data visually and retrieve data from different sources by modifying code, notebooks are also entering the realm of business intelligence software.

Notable examples 
Example of projects or products of notebooks:

Free/open-source notebooks
 Apache Zeppelin — Apache License 2.0
 Apache Spark Notebook — Apache License 2.0
 IPython — BSD
 Jupyter Notebook (formerly IPython) — Modified BSD License (shared copyright model)
Google Colaboratory — No setup Jupyter notebook environment — Free software
Amazon SageMaker --- ML Focused Jupyter notebook environment --- Free Basic Access
Pycharm Notebook Integration - jupyter notebook interface/frontend notebooks for Jetbrains IDEs, this is a premium feature but source code can be found here
VSCode Notebook Support - jupyter notebook interface/frontend and API for VSCode
 JupyterLab — Revised BSD License
Starboard - A shareable In-browser literal notebook, source code can be found here
 Mozilla Iodide — MPL 2.0; development in alpha stage
 R Markdown — GPLv3
 SageMath — GPLv3
 Org-mode on emacs (with the built-in babel addon) — GPL
 Xamarin Workbooks for DotNet — MIT
 Polynote Apache License 2.0
GNU TeXmacs (a document processor which can act as notebook interface as well) — GPLv3
Javalí Notebooks: Java based notebooks environment and LMS with debugging and unit test support, designed for the academy, a presentation video can be found here.,

Partial copyleft
 SMath Studio — Freeware, not libre: licensed under Creative Commons Attribution-No Derivatives

Proprietary notebooks
 Wolfram Mathematica
 Mathcad 
 Noteable
Noteable
 Deepnote
 Carbide
 Databricks cloud (founded 2013).
 Datalore
 Nextjournal
 Observable — Uses open-source components, but the look and feel are proprietary
 WolframAlpha Notebooks

References 

 
Graphical user interfaces
Literate programming
Technical communication tools