How can i check whether user is logged in or not in magento 2.0

To check if customer is loged in or not you can call Magento\Customer\Model\Session::isLoggedIn() method.

If you want to do that properly in *.phtml files you should use helper inside the template. Object manager is not preferred way to call models inside template files. So I am not recommending to follow this post There isn't core helper that can be reused so you need to create new one.

<?php
namespace YourCompany\ModuleName\Helper;

class Data extends \Magento\Framework\App\Helper\AbstractHelper
{
    public function __construct(
        \Magento\Framework\App\Helper\Context $context,
        \Magento\Customer\Model\Session $customerSession
    ) {
        $this->customerSession = $customerSession;
        parent::__construct($context);
    }

    public function isLoggedIn()
    {
        return $this->customerSession->isLoggedIn();
    }
}

Then in your *.phtml file you can call your helper and call isLoggedIn method like this:

<?php $helper = $this->helper('YourCompany\ModuleName\Helper\Data'); ?>
<?php if($helper->isLoggedIn()) : ?>
    logged in
<?php else : ?>
    not logged in
<?php endif; ?>

This is for only Magento 2.0, add this in phtml file:

$objectManager = \Magento\Framework\App\ObjectManager::getInstance();
$customerSession = $objectManager->create('Magento\Customer\Model\Session');

Check via following:

if($customerSession->isLoggedIn()){
   // your code
}

If you want to get user logged in at template level phtml, you can call :

<?php $_loggedin = $this->helper('Magento\Checkout\Helper\Cart')->getCart()->getCustomerSession()->isLoggedIn(); ?>