Please note that the informations below could be outdated. All the latest and updated instructions can be found here: https://www.arduino.cc/en/Guide/Linux
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Open Ubuntu Software Center and search for Arduino. Alternatively, you can install via the command line by running the following in a Terminal
sudo apt-get update && sudo apt-get install arduino arduino-core
The above installs a package from the Ubuntu software repositories, which currently is the old Arduino version 1.0.5.
A new version of the Arduino can be downloaded from the Arduino website. After downloading it can be unpacked anywhere, and it should run out of the box (tested August 8 2013 with Uno R3, December 25 2015 with LilyPad USB).
Using this method Arduino software won't automatically be updated, so you should check Arduino website every few months and download a new version if one is available. You will also have to start the Arduino application by opening the folder where you unpacked it to (or integrate it with Ubuntu by providing a .desktop file). You won't find it in the same place where other applications of your Ubuntu computer are. Hopefully the Ubuntu package repositories will catch up to solve this unconvenience.
An arduino package is available in the "universe" repository of Ubuntu. Use the "Ubuntu Software Center" (or your favorite package manager, i.e. synaptic or apt-get) to install the package "arduino." Available on all architectures. For more information see the Debian entry in Playground. IMPORTANT NOTE: The "Arduino IDE" package in the Ubuntu 10.10 (Maverick) repository is version 18 and does not support the latest Arduino UNO, see below.
the Ubuntu repositories are a long way behind, so the default package in Maverick does not support those boards. Version 0018 of the IDE is from January 2010, the Uno and Mega2560 were released in September/October 2010.
To install, you have to enable the maverick-backports repository in the "Ubuntu Software Center" settings or do the following:
sudo dpkg -i *.deb
Alternatively, you can use:
Easy walkthrough with lots of screen shots of the official IDE from the main Arduino site. If you have a Uno or Mega 2560 go here first. The repository version 0018 does not work with these later boards. This is for 32 & 64 bit Ubuntu 10.10 but should work will all versions after 9.04,ideal you're new to Ubuntu."Complete Numpties Guide to Arduino on Ubuntu"
You can always install the newest version of Arduino from Debian unstable. Just download the .debs for arduino, arduino-core, and librxtx-java and double click on them or:
sudo dpkg -i *.deb
Tested with Ubuntu 10.04 LTS and Ubuntu 10.10, but should work with older releases.
sudo apt-get install gcc-avr avr-libc
sudo usermod -aG dialout <myuser>