Responsive Web Design (RWD) essentially indicates that a web site is crafted to use W3C CSS3 media queries with fluid proportion-based grids, to adapt the layout to the viewing environment, and probably also flexible images. As a result, users across a broad range of devices and browsers will have access to a single source of content, laid out so as to be easy to read and navigate with a minimum of resizing, panning and scrolling.
"Mobile First" and "Progressive Enhancement" (thought processes/strategies for when a new site layout is being considered) are related concepts that predated RWD: browsers of basic mobile phones do not understand media queries, so it is wise to create a basic web site then enhance it for smart phones and PCs — rather than attempt "graceful degradation" to try to degrade a complex, image-heavy site to work on the most basic mobile phones. Luke Wroblewski has summarized some of the RWD and mobile design challenges, and created a catalog of multi-device layout patterns.
Ethan Marcotte coined the term Responsive Web Design (RWD) in his article in A List Apart. He describes the theory and practice of responsive web design in his brief book on the subject. .net Magazine chose Responsive Design as #2 on its list of Top Web Design Trends for 2012 (Progressive Enhancement was #1), and listed 20 of Ethan Marcotte's favorite responsive sites.
Since Ethan Marcotte's original book on the subject, another book has addressed the subject in specific reference to HTML5 and CSS3; 'Responsive web design with HTML5 and CSS3' by Ben Frain . 'Implementing Responsive Design: Building sites for an anywhere, everywhere web'  by Tim Kadlec should also tackle the subject but is not yet released (due August 16, 2012).
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