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1. c4 c5 2. Nf3 Nc6 3. Nc3 Nf6 4. g3 d5 5. d4 dxc4 
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better was e6 to consolidate your centre and prevent d5
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6. d5 Nb4 7. e4 
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and now the centre is mine
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7... b5 
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there are more important things to do than protect c4. eg Bg4 or Nd3+ 
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8. a3 Qa5 9. e5 Nfxd5 
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should take with the other N - Nbxd5. gets your N out of trouble and opens a diagonal to the K for your Q
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10. axb4 Qxa1 
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correct was Nxc3 offering a Q swap. But taking the R is a really bad move. When a piece is offered for free then you should look for the hook inside it.
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11. Nxd5 Bd7 
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better was f6 opening an escape line for the K
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12. Nc7+ Kd8 13. e6 Kxc7 
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just sets things up for a check with discovered attack on the Q. Desperation measure was Qxc1 getting rid of my B and forcing the Q off the d-file
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14. Bf4+ Kb6 
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better was Kd8 or Kb7 Puts the K in a better place
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15. Qxa1 
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and now whatever you play it is soon mate
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15... Bxe6 16. Qa5+ Kc6 17. Qc7+ Kd5 18. Qb7# 
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