Transcribed from the product's home page:
"Brackets is a modern, open source text editor that understands web design."
"With focused visual tools and preprocessor support, Brackets is a modern text editor that makes it easy to design in the browser. Try Creative Cloud Extract (preview) for Brackets for an easy way to get clean, minimal CSS straight from a PSD with no generated code.
"The Extract for Brackets (Preview) extension lets you pull out design information from a PSD including colors, fonts, gradients, and measurement information as clean, minimal CSS via contextual code hints. You can also extract layers as images, use information from the PSD to define preprocessor variables, and easily get dimensions between objects. All in the context of your code."

Ways to download the editor:

I take a look at the active and available repos in the system:
$ sudo nano /etc/apt/sources.list
$ apt-cache search 'brackets'
The package is not found in the Debian repos nor repos web site, so I am not going to setup the repos.

I visit: http://brackets.io/
The page instantly shows you what DEB package to download.
Install the DEB package:
$ sudo dpkg -i Brackets.1.3.Extract.64-bit.deb
$ sudo apt-get -f install
$ sudo dpkg -i Brackets.1.3.Extract.64-bit.deb

The second way offered is to go to: https://github.com/adobe/brackets/releases
Today, the latest version in the Git hosting is: Brackets.Release.1.3.64-bit.deb

At this point I couldn't install the editor following any of these regular procedures. There's an issue with Debian which has been logged on the GitHub.
Reference:
Web: https://github.com/adobe/brackets/issues/4816

The only way that works is to compile the program from a working PPA package of Ubuntu:
Reference:
Topic: Install Brackets from Ubuntu PPA:
Web: http://www.webupd8.org/2013/11/install-brackets-in-ubuntu-via-ppa-open.html

Go to search the program as a PPA: https://launchpad.net/ubuntu/+ppas
Search for "Brackets".
Click on the section " View package details".
The web is going toe take you here: https://launchpad.net/~webupd8team/+archive/ubuntu/brackets/+packages
On the page, expand the section to view the list of packages.
There is a package for the 64bit computer architecture, recognized by the name string "amd64".
RIGHT CLICK and select "Copy Link location" on the proper files to download the them, like this:
$ wget -c https://launchpad.net/~webupd8team/+archive/ubuntu/brackets/+files/brackets_1.3.0libgcrypt11-16022%2B1%7Eextract%7Ewebupd8%7E0_amd64.deb https://launchpad.net/~webupd8team/+archive/ubuntu/brackets/+files/brackets_1.3.0libgcrypt11-16022%2B1%7Eextract%7Ewebupd8%7E0.dsc https://launchpad.net/~webupd8team/+archive/ubuntu/brackets/+files/brackets_1.3.0libgcrypt11-16022%2B1%7Eextract%7Ewebupd8%7E0.debian.tar.xz https://launchpad.net/~webupd8team/+archive/ubuntu/brackets/+files/brackets_1.3.0libgcrypt11.orig.tar.xz
The option -c  of wget is going to resume a package partially downloaded. See the man of the program:
$ man wget
In order to compile the program I must prepare the build environment. I already prepared one to the installation of the program "SimpleScreenRecorder". Take a look at my guides here:
References:
Guides:
Build packages from source
SimpleScreenRecorder

Remove the screenrecorder remaining directory, and then re-create the new temporary directory:
$ cd /
Remove the directory:
$ sudo rm -rf /wrk
Create the working directory:
$ sudo mkdir wrk
$ sudo chmod 777 wrk
$ ls -hal /
$ cd wrk
Copy the files downloaded to the current directory:
$ cp -dpR brackets_1.3.0libgcrypt11-16022+1~extract~webupd8~0.dsc brackets_1.3.0libgcrypt11-16022+1~extract~webupd8~0_amd64.deb brackets_1.3.0libgcrypt11-16022+1~extract~webupd8~0.debian.tar.xz brackets_1.3.0libgcrypt11.orig.tar.xz /wrk

The process downloads some files from the repositories. Please double check the repos are ok with in the repos file:
$ nano /etc/apt/sources.list

Build for jessie, so set-up the command accordingly:
$ sbuild -d jessie *.dsc

According to the process, the packages to install are:
The following extra packages will be installed:
bsdmainutils debhelper file gettext gettext-base groff-base intltool-debian
libasprintf0c2 libcroco3 libffi6 libglib2.0-0 libmagic1 libpipeline1
libunistring0 libxml2 man-db po-debconf
Suggested packages:
wamerican wordlist whois vacation dh-make gettext-doc groff less www-browser
libmail-box-perl
Recommended packages:
curl wget lynx-cur autopoint libasprintf-dev libgettextpo-dev
libglib2.0-data shared-mime-info xdg-user-dirs xml-core
libmail-sendmail-perl
The following NEW packages will be installed:
bsdmainutils debhelper file gettext gettext-base groff-base intltool-debian
libasprintf0c2 libcroco3 libffi6 libglib2.0-0 libmagic1 libpipeline1
libunistring0 libxml2 man-db po-debconf sbuild-build-depends-brackets-dummy

At the end of the process a summary shows up with the message:
Status: successful

List the directory:
$ ls
Output:
brackets_1.3.0libgcrypt11-16022+1~extract~webupd8~0_amd64-20150602-1711.build
brackets_1.3.0libgcrypt11-16022+1~extract~webupd8~0_amd64.build
brackets_1.3.0libgcrypt11-16022+1~extract~webupd8~0_amd64.changes
brackets_1.3.0libgcrypt11-16022+1~extract~webupd8~0_amd64.deb
brackets_1.3.0libgcrypt11-16022+1~extract~webupd8~0.debian.tar.xz
brackets_1.3.0libgcrypt11-16022+1~extract~webupd8~0.dsc
brackets_1.3.0libgcrypt11.orig.tar.xz


Install the package with gdebi:
$ sudo gdebi *.deb
Output:
Brackets
 Brackets is an open-source editor for web design and development
 built on top of web technologies such as HTML, CSS and JavaScript.
 The project was created and is maintained by Adobe, and is released
 under an MIT License.
Do you want to install the software package? [y/N]: y and then PRESS ENTER.

Run the application:
$ brackets

To install Brackets, you can optionally build a release since Grunt:
References:
Keywords: "install brackets since grunt"
Topic: Many links on where to go to look for Brackets.
Web: https://github.com/adobe/brackets/wiki/Linux-Version
Topic: How to setup grunt
Web: https://github.com/adobe/brackets/wiki/Grunt-Setup
Topic: How to build Brackets releases with Grunt:
Web: https://github.com/adobe/brackets/wiki/Building-Brackets-Releases
Web: https://github.com/adobe/brackets-shell/wiki/Building-brackets-shell

Brackets extensions:

An extension for Brackets that adds items to the context menu for Gruntfile.js to run tasks or sub-tasks. You can run any tasks from the Grunt file from the main Project menu, or the context menu for the Gruntfile.js entry. Or, to run the default task(s), just hit F6.
References:
Web: https://github.com/dhategan/brackets-grunt
Web: https://github.com/markrendle/brackets-grunt

Extract for Brackets (Preview) (non-free):
Adobe - Preview of Extract functionality inside Brackets. Extract design information and assets from a design comp via contextual code hints for CSS.
References:
Web: https://helpx.adobe.com/creative-cloud/help/extract-for-brackets.html