Last year, my Google rankings dropped. In order to rank again, I did SEO for the whole winter (and now my rankings are even better than before).
If you also need to improve your Google ranking, are here the SEO tools that I do recommend:
A tool that gives you a large checklist of things you need to improve:
http://seositecheckup.com/
Checks all your HTML errors:
https://validator.w3.org/
Measures your page speed:
https://developers.google.com/speed/pagespeed/insights/
Improving not only lets you rank higher in Google, your conversion will also rise.
Sitemap generator:
http://www.web-site-map.com/xml_sitemap.php
Gives you a list of your site's broken links:
http://www.brokenlinkcheck.com/broken-links.php
Moz pro's spam score tool:
https://moz.com/researchtools/ose/spam-analysis/
Find related search terms:
https://moz.com/explorer
Is your site mobile friendly?
https://www.google.de/webmasters/tools/mobile-friendly/
80/20 rule: 80% of your traffic is coming from 10-20% of your pages. Only focus on those pages and ignore the rest. That will save you lots of time.
For your most important pages: Watch recordings of your visitor's behaviours and a heatmap that shows you your visitor's clicks using the hotjar tool. (Not really an SEO tool, but you will learn so much about your visitors!)
https://www.hotjar.com
For Firefox or Chrome: The extension "Site Speed Monitor".
Measures the loading time of every site you visit.
And lastly: In Chrome, press Control + Shift + i,
click on >> and then on "Security" and "PageSpeed".
PageSpeed gives you a detailed list of everything that
slows down your page.
After that, hire an SEO consult for a day.
Thanks for the share, nice list for sure!
Thank you very much for this cool share!
Great list. Thanks for sharing.
Really cool list! Just checked it out and we have some work to do 
Nice list, I'll add these -
Track your keywords ranking regularly. It's important to know whether your efforts are paying off and where they are doing harm to your sites visibility.
Rank trackers - RankTrackr, Serpbook, Semrush.
Examine competitor sites. Analyze how competing sites and higher ranking sites are strategized and structured in comparison to yours. Consider the keywords they target, the links they receive, what type of content they publish, their social media presence, and the like. Use this information to try and improve your own site.
Competitor analysis sites - Semrush, Quantcast, Alexa, Open Site Explorer, Majestic Seo & SimilarWeb.
Review your own site. It is important to do this on a regular basis; therefore, you should schedule a routine audit of your own site to ensure that everything is working properly. Be sure to check site speed, links, codes, content, formatting, etc. to ensure that everything is accurate and well-optimized.
Site optimization tools - Quick Sprout, WooRank, Hubspot Website Grader, Traffic Travis, SeoOptimizer.
Thanks for the share, nice list for sure! 
thnx
Thanks for the list tho. Will used it further on