Suppose If I have a concentric rings as in image 1, then how to connect the vertices among the rings efficiently, so that I can achieve what is in image 2
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1If they have the same amount of vertices try selecting all rings and Bridge Edge Loops – Mr Zak Mar 03 '16 at 11:36
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2I edited your post, because in Blender, the designation merging is used for a different operation than you are asking for. Merging is the act of taking two or more vertices, and combining them into a single vertex. – brasshat Mar 03 '16 at 17:24
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You can create a surface from edge rings using the Looptools Loft tool or use Blender's default operator Bridge Edge Loops.
LoopTools addon
If you don't have the Looptools enabled, enable them through the user preferences:

To use the Loft tool, select your loops in the order you want to connect them (the order is important).
Then either go to the Tools panel on the left --> Looptools --> Loft (as seen in the gif above).
Or: open the specials menu using W --> Looptools --> Loft.
Bridge Edge Loops
Select edge loops, press Ctrl+E > Bridge Edge Loops (or find it in menu of 3D View header: Mesh > Edges > Bridge Edge Loops).


