Train from Budapest to Martin (Slovakia)

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hello I'd like to ask if there is a train that goes from budapest to martin ..... i will have to do this journey in the end of july or in the beginning of august!! I' d like to be informed about the timetable and the price of the ticket (I'm a student) thank you

The answer to your question a bit depends on desired time of departure from Budapest or arrival to Martin (since depending on time of the day there is a number of routes and connections) and also whether you need to go only one-way or return?

In case you need to go there and back, then it might make sense not to deal with separate ticket for Hungarian and Slovak legs, but simply buy return international ticket Budapest-Martin (depending on route from 31 to 43 euro). But if you need to travel only one-way, then obviously it will make sense to have separate domestic tickets till the border and from the border (meaning instead of more expensive one-way international ticket).
If to start with a later possibility, then suggestion would be something like: either catch domestic train Budapest-Esztergom (hour and a half, 1120 HUF), then walk over the bridge to Slovak Sturovo (see google maps), or domestic train Budapest-Szob (hour-hour and a half, 1300 HUF)+cross-border ticket Szob-Sturovo for 1,8 euro. Then depending on time of the day you have a number of routes for leg between Sturovo and Martin: a) cheapest and fastest is via Cata-Levice-Hronska Dubrava (at least two changes and 8,65 euro when ticket bought in Slovakia); b) via Nové Zámky-Topoľčany-Prievidza, at least 3 changes and 9,8 euro); c) via Bratislava-Zilina-Vrútky, at least two changes and 14,69 euro. To get a better understanding of routes between Sturovo and Martin we suggest to check Slovak rail network map

thank you for the early answer! I am interested in the international budapest-martin ticket. my ticket will be on return. In case ( which is the most possible) which I will be arriving in Budapest at 12.30 in the first of August ,then  i would like to know the timetable : budapest-martin for that specific day. And in order to know what time to choose I'd like to be informed about the process : arriving to the budapest's airport, getting a transport to the station (a bus maybe) , the name of the train station and the distance from the airport and how long the route bud-martin takes

my return will be from martin to budapest in the 28th of august so that in the 29th of august at 04.00 (4 am) i will be in the airport. Any information you think it will help me will be apreciated... Again thank you very much

In case ( which is the most possible) which I will be arriving in Budapest at 12.30 in the first of August ,then  i would like to know the timetable : budapest-martin for that specific day.

Ok, this will be a bit tricky, but let's try to go step-by-step.
'Tricky' because train to Slovakia that you need to catch departs Budapest-Keleti station at 13:25, which leaves you not a lot of time to get from airport to the station. In case of arrival 12:30 (FR 5028?) buses #200 from Budapest Airport Terminal 2 leave at 12:36, 12:48, 13:00 etc., road to the nearest metro station (Kőbánya-Kispest) takes 24 min. Then Metro (Line 3) train will take you to Deak Ferenc Ter station (app. 16 min.) where you change to line 2 train towards Keleti (another 5 min). Taking into consideration that you'll need to buy tickets for the bus and metro + then complicated international ticket Budapest-Martin + orient around new setting...doubt you can manage to be on time for 13:25 train, unless your flight be early like 30 min. or more.
Next direct train to Slovakia leaving at 15:25 isn't really a good option, since from it you miss last connections (both from Sturovo and Bratislava) to Martin, so doubt you want to spend night somewhere in Slovakia and arrive to Martin in the morning. But honestly we having trouble finding plan B, maybe not to opt for rail option, but from Kőbánya-Kispest metro station go to Arpad hid station (24 min.) where to catch 13:20 bus to Esztergom, it arrives there at 14:30, thus giving you app. 45 min. to cross the bridge and get to Sturovo train station, from where at 15:16 leaves needed train towards Levice (with further change there to Martin) or go totally different direction, try to catch train from Budapest to Komarom (dep. from Deli station at 13:21 or Kelenföld station at 13:28), arr. to Komarom 14:44, then you have almost an hour to cross the bridge to Slovakia (Komarno) from where there is a train towards Hronská Dúbrava-Martin at 15:37 (change in Hronská Dúbrava and arr. to Martin 20:46). Obviously in last two scenarios international ticket is useless, so just will need to use point-to-point.

...from martin to budapest in the 28th of august so that in the 29th of august at 04.00 (4 am) i will be in the airport.

This one is already easier  For instance 14:55 bus to Levice (arr. 17:05), then train to Sturovo (19:00-20:11), cross the bridge to Esztergom and catch train or bus to Budapest (run till 22). Or train to Banska Bystrica (16:06-17:07) and then direct Orangeways bus to Budapest (18:10-22:00) etc.

    wow!! that sounds risky and I'm not sure that i can do this..... I think I'll change my plans.... maybe vienna bratislava martin will be easier for me. Or maybe vienna martin international ticket for the 31st of july and then return in the 27th of august. Let's try this... If I am in vienna airport at 10 am what do you suggest;

...that sounds risky and I'm not sure that i can do this

Yep, especially if you aren't familiar with Budapest city transport. Maybe the safest solution will be just to stay overnight in Budapest and continue to Slovakia in the morning (also will give you some time to see Budapest)

Or maybe vienna martin international ticket for the 31st of july and then return in the 27th of august. Let's try this... If I am in vienna airport at 10 am what do you suggest

Not sure that international ticket Vienna-Martin-Vienna is best solution though, since on relation Austria-Slovakia return tariff is much less attractive. We would suggest something like: Vienna-Bratislava by bus (7 euro for one-way ticket), then Bratislava-Martin by train/bus and same thing on the way back.
So if you can start from Vienna at around 10am, then itinerary would look something like Vienna Airport - Bratislava bus (10:30-11:30, http://www.slovaklines.sk/index_en.html), then either 11:57 train to Vrútky (arr.15:03), while there you change to Vrútky-Martin train (15:09-15:18), one through ticket is 9,98 euro, or direct bus Bratislava-Martin (12:00-16:40), 10,7 euro. In case you late for either, then next train towards Martin leaves Bratislava at 13:37, or next bus at 12:30. As you can see, nothing to worry about when departing from Bratislava during the day - direct or with change connections both by rail or bus available like every half an hour.   

ok thank you for everything!! I will do this one!!  vienna-bratislava- martin!!

It's your choice, if flight to Vienna isn't essentially more expensive, then option Vienna-Bratislava-Martin sound a bit better, meaning avoiding all the hassle (or extra night) with Budapest option. Also, just as reminder, all the train timetables for Slovakia can be checked on ZSSK website, while for buses on http://cp.atlas.sk/