Edinburgh is the capital of Scotland (UK) and a major financial and tourist hub. From Amsterdam it is some 660km away over the North Sea.
Here is an overview of the various travel options between the 2 cities - we will consider air, rail, coach and ferry...
1. Amsterdam-Edinburgh by Air
Flying is the easiest and most convenient travel option between the 2 cities. Scheduled flight time between Amsterdam Schiphol (AMS) and Edinburgh Airport (EDI) is around 1 hour 30 minutes.
Dutch airline KLM (Skyteam) flies up to 6x daily using a mix of Boeing 737s (KLM) and Embraer 190s (KLM Cityhopper). The cheapest return flights start at around €110 from Amsterdam or £80 from Edinburgh - these are base fares and do not include optional extras such as checked luggage.
No frills airline Easyjet flies up to 3x daily between Amsterdam and Edinburgh - prices can be a little bit cheaper than KLM if booking in advance.
2. Amsterdam-Edinburgh by Train
It is possible to travel from Amsterdam to Edinburgh by train in about 10 hours.
From Amsterdam the journey has 3 components - travelling Amsterdam to Brussels Zuid/Midi by Thalys, taking a Eurostar train from Brussels Zuid/Midi to London St Pancras and then taking a UK domestic train from nearby London Kings Cross to Edinburgh.
See here for more info about travel from Amsterdam to London and Amsterdam to Brussels. You would need to purchase separate tickets for this trip - expect to pay from €59 for travel from Amsterdam to London.
Virgin Trains East Coast operate regular direct rail services from London Kings Cross to Edinburgh and this journey takes around 4 hours 20 minutes, stopping in Newcastle, York and a few other towns. There are a huge variety of rail fares in the UK so you could pay as little as £25 for a standard class single (if booking well in advance) right up to £140.
First class singles start from £55 one way - a hot meal and drinks are served at your seat.
Now whether you would do the entire Amsterdam-Edinburgh rail journey in one go is up to you - it would probably be prudent to add a stopover in London to minimise risk of missing the connection.
3. Amsterdam-Edinburgh by Coach
It is also possible to do the journey by coach via London although it will be a long-haul. Eurolines operate a 4x daily coach service from Amsterdam Duivendrecht to London Victoria - 2 by day and 2 overnight services - this trip takes about 11 hours. Flixbus also operates a 2x daily coach service between Amsterdam Sloterdijk and London.
National Express and Megabus UK both operate regular coach services between London Victoria and Edinburgh with a journey time of 9 hours for direct services.
Obviously you could also consider a rail-coach combination - such as coach from Amsterdam to London then a train up to Edinburgh.
4. Amsterdam-Edinburgh by Ferry/Train
Every night a DFDS Seaways ferry runs between Amsterdam Ijmuiden and Newcastle North Shields. This trip takes about 15 hours and cabins start at £74.
A shuttle coach runs to Ijmuiden port from Amsterdam Central.
At North Shields port take the bus to Newcastle station. From there you could travel on an Virgin Trains East Coast or Crosscountry train up to Edinburgh - this takes about 90 minutes and singles start at £9.