Yes you can download Youtuube videos in Raspberry Pi and use for offline viewing.

Software availabe for downlaoding videos is

youtube-dl

you can install using

apt-get install youtube-dl (run this command as root)

After installing this you can download the video

youtube-dl <youtube URL>

if you want to download in mp4 or any specific format then  use the following option

format code extension resolution  note 
171         webm      audio only  DASH webm audio , audio@ 48k (worst)
140         m4a       audio only  DASH audio , audio@128k
160         mp4       192p        DASH video 
133         mp4       240p        DASH video 
134         mp4       360p        DASH video 
135         mp4       480p        DASH video 
136         mp4       720p        DASH video 
137         mp4       1080p       DASH video 
17          3gp       176x144     
36          3gp       320x240     
5           flv       400x240     
43          webm      640x360     
18          mp4       640x360     
22          mp4       1280x720    (best)

youtube-dl -f 18 <Youtube URL>

This command was not working and giving error in my Pi and asked me to upgrade.

If you get error

[youtube] Setting language
 [youtube] bzSTpdcs-EI: Downloading webpage
 [youtube] bzSTpdcs-EI: Downloading video info webpage
 [youtube] bzSTpdcs-EI: Extracting video information
 [youtube] bzSTpdcs-EI: Encrypted signatures detected.
 ERROR: Signature extraction failed: Traceback (most recent call last):
 File "/usr/lib/python2.7/dist-packages/youtube_dl/extractor/youtube.py", line 479, in _decrypt_signature
 video_id, player_url, s
 File "/usr/lib/python2.7/dist-packages/youtube_dl/extractor/youtube.py", line 356, in _extract_signature_function
 raise ExtractorError('Cannot identify player %r' % player_url)
 ExtractorError: Cannot identify player u'/yts/jsbin/player-vflAAoWvh/en_US/base.js'; please report this issue on https://yt-dl.org/bug . Be sure to call youtube-dl with the --verbose flag and include its complete output. Make sure you are using the latest version; type youtube-dl -U to update.
 ; please report this issue on https://yt-dl.org/bug . Be sure to call youtube-dl with the --verbose flag and include its complete output. Make sure you are using the latest version; type youtube-dl -U to update.

You need to upgrade youtube-dl, you can use following command

root@raspberrypi:~# youtube-dl -U
 It looks like you installed youtube-dl with a package manager, pip, setup.py or a tarball. Please use that to update.
 root@raspberrypi:~#

If you get above error then

try running command pip if it gives error and pip is also not installed then install pip and upgrade youtube-dl

root@raspberrypi:~# pip
 -su: pip: command not found
 root@raspberrypi:~# apt-get install python-setuptools
 Reading package lists... Done
 Building dependency tree
 Reading state information... Done
 The following NEW packages will be installed:
 python-setuptools
 0 upgraded, 1 newly installed, 0 to remove and 28 not upgraded.
 Need to get 242 kB of archives.
 After this operation, 770 kB of additional disk space will be used.
 Get:1 http://mirrordirector.raspbian.org/raspbian/ jessie/main python-setuptools all 5.5.1-1 [242 kB]
 Fetched 242 kB in 1s (200 kB/s)
 Selecting previously unselected package python-setuptools.
 (Reading database ... 35818 files and directories currently installed.)
 Preparing to unpack .../python-setuptools_5.5.1-1_all.deb ...
 Unpacking python-setuptools (5.5.1-1) ...
 Setting up python-setuptools (5.5.1-1) ...
 root@raspberrypi:~# easy_install pip
 Searching for pip
 Reading https://pypi.python.org/simple/pip/
 Best match: pip 9.0.1
 Downloading https://pypi.python.org/packages/11/b6/abcb525026a4be042b486df43905d6893fb04f05aac21c32c638e939e447/pip-9.0.1.tar.gz#md5=35f01da33009719497f01a4ba69d63c9
 Processing pip-9.0.1.tar.gz
 Writing /tmp/easy_install-HWeUGq/pip-9.0.1/setup.cfg
 Running pip-9.0.1/setup.py -q bdist_egg --dist-dir /tmp/easy_install-HWeUGq/pip-9.0.1/egg-dist-tmp-yuuYOs
 /usr/lib/python2.7/distutils/dist.py:267: UserWarning: Unknown distribution option: 'python_requires'
 warnings.warn(msg)
 warning: no previously-included files found matching '.coveragerc'
 warning: no previously-included files found matching '.mailmap'
 warning: no previously-included files found matching '.travis.yml'
 warning: no previously-included files found matching '.landscape.yml'
 warning: no previously-included files found matching 'pip/_vendor/Makefile'
 warning: no previously-included files found matching 'tox.ini'
 warning: no previously-included files found matching 'dev-requirements.txt'
 warning: no previously-included files found matching 'appveyor.yml'
 no previously-included directories found matching '.github'
 no previously-included directories found matching '.travis'
 no previously-included directories found matching 'docs/_build'
 no previously-included directories found matching 'contrib'
 no previously-included directories found matching 'tasks'
 no previously-included directories found matching 'tests'
 Adding pip 9.0.1 to easy-install.pth file
 Installing pip script to /usr/local/bin
 Installing pip2.7 script to /usr/local/bin
 Installing pip2 script to /usr/local/bin

Installed /usr/local/lib/python2.7/dist-packages/pip-9.0.1-py2.7.egg
 Processing dependencies for pip
 Finished processing dependencies for pip

root@raspberrypi:~# pip install --upgrade youtube-dl
 Collecting youtube-dl
 Downloading youtube_dl-2017.8.18-py2.py3-none-any.whl (1.6MB)
 100% |████████████████████████████████| 1.6MB 76kB/s
 Installing collected packages: youtube-dl
 Found existing installation: youtube-dl 2014.8.5
 DEPRECATION: Uninstalling a distutils installed project (youtube-dl) has been deprecated and will be removed in a future version. This is due to the fact that uninstalling a distutils project will only partially uninstall the project.
 Uninstalling youtube-dl-2014.8.5:
 Successfully uninstalled youtube-dl-2014.8.5
 Successfully installed youtube-dl-2017.8.18

After all above steps you can download videos

youtube-dl -f 10 <URL>

it will download the videos, after download you can view

omxplayer <Video_downloaded>