The following Wikipedia map depicts the world exports of natural gas. With blue lines you can see the exports made through pipeline networks, and with red the exports of liquefied gas made by ships (LNG).
The lines do not show pipelines or routes. They simply show flows of natural gas exports. Therefore you should only look at which country a line starts, and at which country the arrow points at. It does not matter which countries are crossed by the lines.
Exports through Pipeline Networks
Russia is the queen of exports through pipeline networks, as you can see from the three lines i.e. 136.2 billion cubic meters, 48.9 cubic meters, and 26.2 billion. I guess the line with the 136.2 billion cubic meters includes Norwegian exports too.
The Netherlands are the largest producer of natural gas in the EU, and it exports gas to the EU, but I guess the map treats the EU as a single geographical region and therefore it does not depicts exports made by the Netherlands.
Azerbaijan exports to Turkey 12 billion cubic meters, and Turkmenistan exports 27.4 billion cubic meters of natural gas to China and another 4.7 billion to Iran.
Algeria exports 30 billion cubic meters of natural gas to Europe. There is only one line from Algeria to Europe, but the line represents exports made by all the Algerian pipelines. Saudi Arabia exports 19.9 billion cubic meters of natural gas to Oman. It might actually be Qatar instead of Saudi Arabia. It is difficult to tell from the map.
Western Canada exports to East United States 78.9 billion cubic meters of gas, while another 25.8 b.c.m. of gas is exported from the eastern part of United States to the eastern part of Canada. The United States export another 18.6 billion cubic meters of gas to Mexico.
Bolivia exports 10.7 billion cubic meters of gas to Brazil.
Export of liquefied natural gas with ships (LNG)
Qatar is the king of LNG exports, with 35.4 billion c.m. to Japan, 29.1 billion to South Korea, 16.1 b.c.m. to India, 8.6 b.c.m. to Taiwan, and 23.8 b.c.m. to Europe.
Australia exports 35.8 b.c.m. of gas to Japan and 24.4 b.c.m. to China. Australia is increasing her production and in the near future she is expected to be the largest exporter of LNG, even though she is not one of the richest countries in reserves.
Nigeria exports 5.6 b.c.m. of gas to Europe and 4.8 b.c.m to Japan.
Russia exports 11.6 b.c.m. to Japan.
Algeria exports 13.4 b.c.m. to Turkey and another 5.6 b.c.m. to Europe.
Venezuela exports 2.2 b.c.m. of LNG to Europe, 2 b.c.m. to USA and 3.6 b.c.m. to Argentina.
Indonesia or Malaysia, I cannot tell which one it is, since they are both exporters of natural gas, exports 6.7 b.c.m. of LNG to South Korea, 4 b.c.m. to Taiwan, and 15.1 b.c.m. to Japan.
I must repeat that you should pay attention to the first and last points of the lines. For example the line from Qatar to Europe i.e. 23.8 billion cubic meters, passes through Africa before reaching Europe, but it only refers to Europe. Moreover I might have made minor mistakes. The point is to get a general idea about who is selling to who and who is buying from whom. That’s what matters in geopolitics. The rest is about accounting.